inverse_ALK: Age-Length Key by the methods based on inverse ALKs
In ALKr: Generate Age-Length Keys for fish populations
Description
Usage
Arguments
Details
Value
References
See Also
Examples
Description
Generation of Age-Length Keys (ALK) using incomplete data,
by methods based on inverse ALKs.
Usage
1
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3
4
5
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8
9
10
11
12
13
14
gascuel(x, fi1, fi2, initial_values, threshold = 1e-04, maxiter = 2000,
age_classes = colnames(x), length_classes = rownames(x), name = "",
description = "")
hoenig_heisey(x, fi1, fi2, threshold = 1e-04, maxiter = 2000,
age_classes = colnames(x), length_classes = rownames(x), name = "",
description = "")
inverse_ALK(x, fi1, fi2, age_classes = colnames(x),
length_classes = rownames(x), name = "", description = "")
kimura_chikuni(x, fi1, fi2, threshold = 1e-04, maxiter = 2000,
age_classes = colnames(x), length_classes = rownames(x), name = "",
description = "")
Arguments
x
A i \times j matrix with i lines
and j columns, where x[i, j] is the count
of individuals of length i and age j.
fi1
A vector of length i where fi[i]
is the number of fish in the length-class i on the
population from which x was sampled.
fi2
A vector of length i where fi[i]
is the number of fish in the length-class i on a
population with unknown age information.
age_classes
A vector with the name of each age
class.
length_classes
A vector with the name of each age
class.
threshold
The value at which convergence is
considered to be achieved: see ‘details’.
maxiter
The maximum number of iterations of the EM
algorithm: see ‘details’.
initial_values
A vector with the initial values
for α, β and γ: see
‘details’.
name
A string with the name of the ALK.
description
A string describing the ALK.
Details
inverseALK calculates an ALK from a sample of
aged-fish, the length distribution of the sampled
population and the length distribution of a population with
unknown age-length data, as described by Clark (1981),
Bartoo and Parker (1983) and Hilborn and Walters (1992).
kimura_chikuni, hoenig_heisey and
gascuel use the same inputs as inverseALK to
calculate an ALK as described respectively by Kimura and
Chikuni (1987), Hoenig and Heisey (1987) and Gascuel
(1994).
hoenig employs the generalized method proposed by
Hoenig et al. (1993, 1994), which takes an undefined
number of data sets with known and unknown age information
and combines them to calculate the ALK.
The returned ALKr object contains information on the
convergence threshold that was used, the number of
iterations ran, and if convergence was reached.
Initial values
The method proposed by Gascuel (1994) is based on the
assumption that the length distribution within each
age class follows a Normal distribution, where the standard
deviation of length at age σ(j) is
given by a linear model as a function of three parameters
α, β and γ:
σ(j) = α + β l(j) +
γ Δl(j)
where Δl(j) is the difference
between the mean lengths at age-class j and
age-class j-1.
Convergence
The methods proposed by Kimura and Chikuni (1987), Hoenig
and Heisey (1987) and Gascuel (1994) are all based on the
EM algorithm as defined by Dempster et al. (1997),
and build the ALK by a series of iterations which are
repeated until convergence is acheived.
The convergence is tested by evaluating the sum of the
absolute differences between the ages distributions
calculated on the previous and current iterations:
sum(abs(pj_prev - pj_curr)). The algorithm exits
when either this value is smaller than the specified
threshold or when the number of iterations reaches
maxiter.
Value
An ALKr object, containing a i \times j matrix
with the probability of an individual of length i
having age j, i.e. P(j|i), a i \times j
matrix with the estimated number of individuals of length
i and age j, and information about the method
used to generate the key.
References
Bartoo, N.W., Parker, K.R. (1983). Stochastic age-frequency
estimation using the von Bertalanffy growth equation.
Fishery Bulletin, 81/1, 91-96
Clark, W.G. (1981). Restricted Least-Squares Estimates of
Age Composition from Length Composition. Canadian
Journal of Fisheries and Aquatic Sciences, 38/3,
297-307. DOI: 10.1139/f81-041
Dempster, A.P., Laird, N.M., Rubin, D.B. (1977). Maximum
Likelihood from Incomplete Data via the EM Algorithm.
Journal of the Royal Statistical Society. Series B
(Methodological), 39/1, 1-38. DOI:
10.2307/2984875
Gascuel, D. (1994). Une methode simple d'ajustement des
cles taille/age: application aux captures d'albacores
(Thunnus albacares) de l'Atlantique Est. Canadian
Journal of Fisheries and Aquatic Sciences, 51/3,
723-733. DOI: 10.1139/f94-072
Hilborn, R., Walters, C.J. (1992). Quantitative fisheries
stock assessment: Choice, dynamics and uncertainty.
Reviews in Fish Biology and Fisheries, 2/2,
177-178. DOI: 10.1007/BF00042883
Hoenig, J.M., Heisey, D.M. (1987), Use of a Log-Linear
Model with the EM Algorithm to Correct Estimates of Stock
Composition and to Convert Length to Age.
Transactions of the American Fisheries Society,
116/2, 232-243. DOI:
10.1577/1548-8659(1987)116<232:UOALMW>2.0.CO;2
See Also
hoenig
Examples
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11
data(hom)
inverse_ALK(hom$otoliths[[1]], fi1 = hom$F1992, fi2 = hom$F1993)
kimura_chikuni(hom$otoliths[[1]], fi1 = hom$F1992, fi2 = hom$F1993) # converges
kimura_chikuni(hom$otoliths[[1]], fi1 = hom$F1992, fi2 = hom$F1993, maxiter = 10) # won't converge
hoenig_heisey(hom$otoliths[[1]], fi1 = hom$F1992, fi2 = hom$F1993)
gascuel(hom$otoliths[[1]], fi1 = hom$F1992, fi2 = hom$F1993,
initial_values = c(0.1, 0.07, 0.06))
Example output
0 1 2 3 4
7 2.153102e+00 -1.171167e+00 1.871984e-02 -6.000848e-02 9.213687e-02
8 2.153102e+00 -1.171167e+00 1.871984e-02 -6.000848e-02 9.213687e-02
9 2.153102e+00 -1.171167e+00 1.871984e-02 -6.000848e-02 9.213687e-02
10 2.153102e+00 -1.171167e+00 1.871984e-02 -6.000848e-02 9.213687e-02
11 2.910497e+00 -2.132581e+00 3.702986e-01 -4.483765e-01 3.236365e-01
12 2.153102e+00 -1.171167e+00 1.871984e-02 -6.000848e-02 9.213687e-02
13 1.281385e+00 -6.463817e-02 -3.859263e-01 3.869799e-01 -1.743053e-01
14 2.673509e-01 1.222545e+00 -8.566356e-01 9.069443e-01 -4.842473e-01
15 2.153102e+00 -1.171167e+00 1.871984e-02 -6.000848e-02 9.213687e-02
16 -9.269517e-01 2.738555e+00 -1.411024e+00 1.519345e+00 -8.492887e-01
17 7.553016e-01 -2.648790e-01 1.121070e+00 -1.756179e+00 1.132965e+00
18 -2.165319e+00 3.246670e+00 1.603356e-01 -8.028364e-01 5.714089e-01
19 -1.321321e-02 7.828098e-02 -1.426248e-01 5.236309e+00 -4.981494e+00
20 2.490383e-01 -1.152376e+00 3.973004e+00 -5.749964e+00 3.566070e+00
21 5.664107e-02 -2.270293e-01 4.891580e-01 2.601567e-01 1.571723e+00
22 5.664107e-02 -2.270293e-01 4.891580e-01 2.601567e-01 1.571723e+00
23 -1.044458e-02 3.939251e-02 -8.940532e-02 -5.394977e-04 5.397472e-01
24 -5.374615e-02 1.553492e-01 -3.558837e-01 4.117349e-01 6.462598e-01
25 -3.976376e-02 1.332669e-01 -3.788722e-01 5.623755e-01 1.108979e+00
26 1.910224e-02 -3.399418e-02 1.133496e-01 -5.184960e-01 8.117601e-01
27 3.189523e-02 -3.377642e-02 1.655256e-01 -1.216013e+00 2.458940e+00
28 7.916112e-02 -2.717065e-01 5.994854e-01 -1.250691e-01 -2.931454e+00
29 3.884537e-04 8.293789e-03 -1.442592e-02 -1.060558e-01 4.286798e-01
30 2.792673e-03 -1.644396e-02 5.432607e-02 -4.492304e-02 -3.653887e-01
31 -3.086370e-02 5.572475e-02 -1.758505e-01 7.804397e-01 -1.252220e+00
32 1.609508e-02 -2.162789e-02 6.072914e-02 -3.907492e-01 9.497298e-01
33 4.754402e-03 -1.331637e-02 9.361678e-03 7.758777e-02 -9.266141e-02
34 1.787657e-02 -4.247241e-02 1.262201e-01 -3.735553e-01 2.714560e-01
35 -8.023094e-04 8.321309e-03 -1.573987e-02 -6.182394e-02 2.869240e-01
36 -1.113901e-02 2.525294e-02 -6.724159e-02 1.947889e-01 -2.011294e-01
37 1.113778e-02 -2.531674e-02 6.777310e-02 -1.963659e-01 1.991232e-01
38 2.404930e-02 -5.452150e-02 1.451757e-01 -4.205525e-01 4.342416e-01
39 -1.601102e-02 4.610215e-02 -1.047601e-01 1.193672e-01 1.868230e-01
40 1.057759e-03 -1.760813e-03 1.227977e-03 -3.200823e-03 3.808406e-02
41 3.812377e-16 -2.088106e-17 1.271024e-16 6.528252e-16 2.592327e-16
5 6 7 8 9
7 -3.469562e-02 -8.209329e-03 1.616737e-02 -1.799939e-04 -1.466226e-02
8 -3.469562e-02 -8.209329e-03 1.616737e-02 -1.799938e-04 -1.466226e-02
9 -3.469562e-02 -8.209329e-03 1.616737e-02 -1.799938e-04 -1.466226e-02
10 -3.469562e-02 -8.209329e-03 1.616737e-02 -1.799938e-04 -1.466226e-02
11 -2.508478e-02 -8.375689e-03 3.913545e-02 1.693911e-02 -5.715149e-02
12 -3.469562e-02 -8.209329e-03 1.616737e-02 -1.799938e-04 -1.466226e-02
13 -4.575712e-02 -8.017858e-03 -1.026751e-02 -1.988306e-02 3.424030e-02
14 -5.862455e-02 -7.795127e-03 -4.101820e-02 -4.280288e-02 9.112677e-02
15 -3.469562e-02 -8.209329e-03 1.616737e-02 -1.799938e-04 -1.466226e-02
16 -7.377946e-02 -7.532800e-03 -7.723553e-02 -6.979722e-02 1.581261e-01
17 -3.114932e-03 1.944843e-02 1.120191e-01 6.742831e-02 -2.107035e-01
18 -2.905152e-02 2.625918e-02 5.463255e-02 2.379077e-02 -1.087657e-01
19 9.924653e-01 2.148380e-03 -6.342199e-01 -9.077433e-02 8.912780e-01
20 7.739616e-02 6.777226e-02 3.403501e-01 2.308546e-01 -6.661022e-01
21 -1.153014e+00 -3.938947e-01 4.199205e-01 -7.319027e-02 -1.924432e-01
22 -1.153014e+00 -3.938947e-01 4.199205e-01 -7.319027e-02 -1.924432e-01
23 -5.325783e-01 1.514622e+00 4.816369e-02 -2.133375e-01 -1.886750e-01
24 8.239541e-02 -2.574033e-01 8.949490e-01 2.267711e-01 -6.856820e-01
25 6.545322e-01 -3.279034e-01 -9.194233e-01 -3.154256e-01 -6.313376e-01
26 1.313052e+00 -1.674162e-01 -1.563312e+00 -1.479172e+00 3.335860e+00
27 -3.719829e-01 -3.331450e-01 2.154869e-01 2.181180e+00 -1.445095e+00
28 3.962141e+00 7.752535e-01 -3.990457e-01 3.836618e-01 -8.818640e-01
29 -9.062469e-01 -8.805334e-02 1.043095e+00 -9.657711e-01 6.452537e-01
30 4.515309e-01 2.821212e-01 -5.318873e-01 -1.190236e-02 5.423833e-01
31 1.299040e-01 1.567422e-01 -1.457354e-01 1.765382e+00 1.394709e+00
32 -2.369568e+00 -1.714453e-01 2.819620e+00 -4.118617e-01 1.169238e+00
33 -3.445830e-02 -1.498705e-01 1.417848e-01 1.774666e+00 -8.023840e-01
34 8.090756e-01 6.056544e-02 -8.510558e-01 -1.623424e-01 -1.392939e+00
35 1.363288e-01 -1.113920e-01 -3.290942e-01 -1.101204e+00 -9.487247e-02
36 5.302499e-01 -2.267010e-02 -6.408978e-01 -5.197730e-01 -1.155242e-01
37 -4.895318e-01 2.401971e-02 5.988359e-01 4.425034e-01 1.087738e-01
38 -1.144818e+00 4.894512e-02 1.383709e+00 1.122198e+00 2.494186e-01
39 1.833874e+00 -2.020683e-01 -2.406054e+00 -1.438512e+00 -2.302220e+00
40 -4.394383e-01 -1.078606e-02 4.626880e-01 7.882276e-01 7.544497e-02
41 -3.881986e-16 8.162052e-17 2.168574e-16 -1.908484e-16 -8.826761e-17
10 11 12 13 14
7 2.294124e-02 -1.241020e-02 -1.068623e-04 1.963470e-03 -3.611497e-03
8 2.294124e-02 -1.241020e-02 -1.068623e-04 1.963470e-03 -3.611497e-03
9 2.294124e-02 -1.241020e-02 -1.068623e-04 1.963470e-03 -3.611497e-03
10 2.294124e-02 -1.241020e-02 -1.068623e-04 1.963470e-03 -3.611497e-03
11 5.258484e-02 -3.584594e-02 -4.873167e-03 7.624506e-03 -8.596809e-03
12 2.294124e-02 -1.241020e-02 -1.068623e-04 1.963470e-03 -3.611497e-03
13 -1.117678e-02 1.456294e-02 5.378870e-03 -4.552044e-03 2.126299e-03
14 -5.086495e-02 4.593976e-02 1.176021e-02 -1.213129e-02 8.800855e-03
15 2.294124e-02 -1.241020e-02 -1.068623e-04 1.963470e-03 -3.611497e-03
16 -9.760862e-02 8.289454e-02 1.927598e-02 -2.105793e-02 1.666197e-02
17 1.648024e-01 -1.171426e-01 -2.109680e-02 2.623911e-02 -2.685163e-02
18 9.483081e-02 -6.015040e-02 -9.435883e-03 1.224157e-02 -1.494492e-02
19 -1.027909e+00 5.873391e-01 4.766471e-02 -1.038030e-01 1.607052e-01
20 4.914915e-01 -3.623367e-01 -7.041685e-02 8.366375e-02 -8.070431e-02
21 5.308087e-01 -2.634704e-01 2.469743e-02 3.404658e-02 -8.384691e-02
22 5.308087e-01 -2.634704e-01 2.469743e-02 3.404658e-02 -8.384691e-02
23 3.336002e-01 -2.545456e-01 -2.883656e-01 1.540107e-01 -5.845855e-02
24 5.118745e-01 -4.942222e-01 -1.538098e-01 1.704648e-01 -1.026555e-01
25 3.472362e-01 5.481309e-01 7.434065e-01 -4.918682e-01 2.191440e-02
26 -3.249965e+00 2.634034e+00 -3.403546e-01 -5.202724e-01 6.372868e-01
27 6.087261e-01 -1.644167e+00 1.512233e-01 4.954144e-01 -2.575280e-01
28 -5.726294e-01 3.075842e-01 7.632936e-02 -1.000023e-01 9.963826e-02
29 3.377810e+00 -1.600943e+00 -7.898843e-01 4.143631e-01 -4.695168e-01
30 -8.486844e-02 -3.829242e-01 1.360392e+00 -4.614107e-02 -1.692309e-01
31 -1.640447e+00 5.756066e-01 -1.040557e+00 2.922549e-02 3.680798e-01
32 -1.851554e+00 1.295082e+00 -2.187204e-01 -2.238582e-01 3.436302e-01
33 1.274128e+00 -2.193410e+00 9.825934e-01 5.298159e-01 -4.775364e-01
34 1.497087e+00 1.651714e+00 4.950962e-01 -1.328737e+00 2.162862e-01
35 8.957068e-01 2.437406e+00 -4.811562e-02 -1.417536e+00 3.954476e-01
36 -2.220930e-01 7.467712e-01 8.023514e-01 1.986511e-01 3.777181e-01
37 2.059248e-01 -6.008317e-01 -7.949488e-01 3.233452e+00 -1.760936e+00
38 4.795025e-01 -1.612291e+00 -1.732290e+00 -4.288910e-01 2.566882e+00
39 2.286890e+00 1.099319e+00 3.988292e+00 -1.743236e+00 -2.552721e-01
40 1.755745e-01 -1.466669e+00 -1.461826e-01 3.509426e+00 -1.937718e+00
41 -2.215838e-18 -1.782157e-17 -5.963917e-17 2.057545e-16 5.164343e-16
15
7 2.119375e-05
8 2.119375e-05
9 2.119375e-05
10 2.119375e-05
11 1.693613e-04
12 2.119375e-05
13 -1.493382e-04
14 -3.477115e-04
15 2.119375e-05
16 -5.813502e-04
17 6.928061e-04
18 3.346198e-04
19 -2.151416e-03
20 2.259677e-03
21 -2.626250e-04
22 -2.626250e-04
23 6.813558e-03
24 3.604001e-03
25 -1.524768e-02
26 8.536757e-03
27 -6.683569e-03
28 -1.483631e-03
29 2.301299e-02
30 -3.983675e-02
31 2.986030e-02
32 5.259866e-03
33 -3.105504e-02
34 5.725726e-03
35 2.044579e-02
36 -7.531552e-02
37 -2.361285e-02
38 -6.075735e-02
39 -9.253340e-02
40 -4.597605e-02
41 1.000000e+00
Method: Classic Inverse ALK
0 1 2 3 4 5 6
7 0.6304005 0.3695995 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
8 0.6304005 0.3695995 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
9 0.6304005 0.3695995 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
10 0.6304005 0.3695995 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
11 0.7189785 0.2810215 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
12 0.6304005 0.3695995 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
13 0.5320734 0.4679266 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
14 0.4222942 0.5777058 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
15 0.6304005 0.3695995 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
16 0.2989382 0.7010618 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
17 0.4333541 0.5081451 0.05850078 0.0000000 0.00000000 0.00000000 0.0000000
18 0.0000000 0.9287200 0.07127996 0.0000000 0.00000000 0.00000000 0.0000000
19 0.1758596 0.4124212 0.28488273 0.1268365 0.00000000 0.00000000 0.0000000
20 0.0000000 0.5914511 0.40854886 0.0000000 0.00000000 0.00000000 0.0000000
21 0.0000000 0.2435485 0.42058195 0.2996047 0.03626485 0.00000000 0.0000000
22 0.0000000 0.2435485 0.42058195 0.2996047 0.03626485 0.00000000 0.0000000
23 0.0000000 0.0000000 0.24176235 0.4305530 0.06948686 0.00000000 0.2581978
24 0.0000000 0.0000000 0.00000000 0.6981634 0.12676100 0.12537196 0.0000000
25 0.0000000 0.0000000 0.18088809 0.6442849 0.11697862 0.05784839 0.0000000
26 0.0000000 0.0000000 0.00000000 0.5539899 0.17881663 0.13264288 0.0000000
27 0.0000000 0.0000000 0.00000000 0.7364744 0.17828917 0.06612581 0.0000000
28 0.0000000 0.0000000 0.00000000 0.2218824 0.05371432 0.39844289 0.1995905
29 0.0000000 0.0000000 0.00000000 0.2575943 0.06235963 0.18502890 0.0000000
30 0.0000000 0.0000000 0.00000000 0.0000000 0.05622025 0.08340629 0.4178040
31 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.2973865
32 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.2735107
33 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.14182476 0.0000000
34 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.5240278
35 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
36 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
37 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
38 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
39 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
40 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
41 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
7 8 9 10 11 12
7 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
8 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
9 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
10 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
11 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
12 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
13 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
14 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
15 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
16 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
17 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
18 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
19 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
20 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
21 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
22 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
23 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
24 0.04970363 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
25 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
26 0.00000000 0.00000000 0.1345506 0.00000000 0.00000000 0.000000e+00
27 0.00000000 0.01911062 0.0000000 0.00000000 0.00000000 0.000000e+00
28 0.12636994 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
29 0.07335459 0.00000000 0.3753800 0.04628254 0.00000000 0.000000e+00
30 0.06613273 0.02410475 0.3384234 0.01390866 0.00000000 3.816275e-09
31 0.00000000 0.13725913 0.4817692 0.03959987 0.04398538 0.000000e+00
32 0.43293049 0.03155980 0.2215450 0.00000000 0.04045399 4.996564e-09
33 0.11245267 0.12296377 0.5754580 0.04730080 0.00000000 6.489228e-09
34 0.00000000 0.18139931 0.0000000 0.13955870 0.15501420 0.000000e+00
35 0.16492593 0.12022785 0.4219906 0.13874509 0.15411048 0.000000e+00
36 0.00000000 0.00000000 0.0000000 0.32258845 0.35831365 4.425612e-08
37 0.00000000 0.24526931 0.0000000 0.28304518 0.47158671 0.000000e+00
38 0.00000000 0.11077422 0.0000000 0.38350631 0.00000000 0.000000e+00
39 0.00000000 0.00000000 0.6616441 0.21754006 0.12081581 5.968893e-08
40 0.00000000 0.15020291 0.5272008 0.13000264 0.19253311 1.189010e-08
41 0.00000000 0.00000000 0.0000000 0.32686114 0.24203969 8.968459e-08
13 14 15
7 0.000000e+00 0.0000000 0.000000e+00
8 0.000000e+00 0.0000000 0.000000e+00
9 0.000000e+00 0.0000000 0.000000e+00
10 0.000000e+00 0.0000000 0.000000e+00
11 0.000000e+00 0.0000000 0.000000e+00
12 0.000000e+00 0.0000000 0.000000e+00
13 0.000000e+00 0.0000000 0.000000e+00
14 0.000000e+00 0.0000000 0.000000e+00
15 0.000000e+00 0.0000000 0.000000e+00
16 0.000000e+00 0.0000000 0.000000e+00
17 0.000000e+00 0.0000000 0.000000e+00
18 0.000000e+00 0.0000000 0.000000e+00
19 0.000000e+00 0.0000000 0.000000e+00
20 0.000000e+00 0.0000000 0.000000e+00
21 0.000000e+00 0.0000000 0.000000e+00
22 0.000000e+00 0.0000000 0.000000e+00
23 0.000000e+00 0.0000000 0.000000e+00
24 0.000000e+00 0.0000000 0.000000e+00
25 0.000000e+00 0.0000000 0.000000e+00
26 0.000000e+00 0.0000000 0.000000e+00
27 0.000000e+00 0.0000000 0.000000e+00
28 0.000000e+00 0.0000000 0.000000e+00
29 0.000000e+00 0.0000000 0.000000e+00
30 0.000000e+00 0.0000000 0.000000e+00
31 0.000000e+00 0.0000000 0.000000e+00
32 0.000000e+00 0.0000000 0.000000e+00
33 0.000000e+00 0.0000000 0.000000e+00
34 0.000000e+00 0.0000000 0.000000e+00
35 0.000000e+00 0.0000000 0.000000e+00
36 1.126047e-04 0.3189852 0.000000e+00
37 9.880152e-05 0.0000000 0.000000e+00
38 8.924608e-05 0.5056302 0.000000e+00
39 0.000000e+00 0.0000000 0.000000e+00
40 6.050605e-05 0.0000000 0.000000e+00
41 1.521283e-04 0.4309470 7.983815e-83
Method: Kimura & Chikuni
Value
ConvergenceThreshold 1e-04
Iterations 193
Converged TRUE
0 1 2 3 4 5 6
7 0.6763306 0.3236694 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
8 0.6763306 0.3236694 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
9 0.6763306 0.3236694 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
10 0.6763306 0.3236694 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
11 0.7581245 0.2418755 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
12 0.6763306 0.3236694 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
13 0.5821229 0.4178771 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
14 0.4724433 0.5275567 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
15 0.6763306 0.3236694 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
16 0.3431394 0.6568606 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
17 0.4728580 0.4525883 0.07455370 0.00000000 0.00000000 0.00000000 0.0000000
18 0.0000000 0.9010484 0.09895157 0.00000000 0.00000000 0.00000000 0.0000000
19 0.1920689 0.3676712 0.36339315 0.07686671 0.00000000 0.00000000 0.0000000
20 0.0000000 0.5029259 0.49707407 0.00000000 0.00000000 0.00000000 0.0000000
21 0.0000000 0.2137092 0.52805636 0.17871534 0.07951912 0.00000000 0.0000000
22 0.0000000 0.2137092 0.52805636 0.17871534 0.07951912 0.00000000 0.0000000
23 0.0000000 0.0000000 0.32408177 0.27420549 0.16267643 0.00000000 0.2390363
24 0.0000000 0.0000000 0.00000000 0.45471805 0.30348917 0.17391525 0.0000000
25 0.0000000 0.0000000 0.24124182 0.40822928 0.27246151 0.07806739 0.0000000
26 0.0000000 0.0000000 0.00000000 0.33768323 0.40067106 0.17220419 0.0000000
27 0.0000000 0.0000000 0.00000000 0.46159915 0.41077570 0.08827353 0.0000000
28 0.0000000 0.0000000 0.00000000 0.12170805 0.10830763 0.46549474 0.1591469
29 0.0000000 0.0000000 0.00000000 0.16695127 0.14856944 0.25541430 0.0000000
30 0.0000000 0.0000000 0.00000000 0.00000000 0.12651337 0.10874822 0.3717968
31 0.0000000 0.0000000 0.00000000 0.00000000 0.00000000 0.00000000 0.2817889
32 0.0000000 0.0000000 0.00000000 0.00000000 0.00000000 0.00000000 0.2309773
33 0.0000000 0.0000000 0.00000000 0.00000000 0.00000000 0.17630151 0.0000000
34 0.0000000 0.0000000 0.00000000 0.00000000 0.00000000 0.00000000 0.4232098
35 0.0000000 0.0000000 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
36 0.0000000 0.0000000 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
37 0.0000000 0.0000000 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
38 0.0000000 0.0000000 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
39 0.0000000 0.0000000 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
40 0.0000000 0.0000000 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
41 0.0000000 0.0000000 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
7 8 9 10 11 12 13
7 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
8 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
9 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
10 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
11 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
12 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
13 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
14 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
15 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
16 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
17 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
18 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
19 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
20 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
21 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
22 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
23 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
24 0.06787752 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
25 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
26 0.00000000 0.00000000 0.08944152 0.00000000 0.00000000 0.00000000 0.00000000
27 0.00000000 0.03935163 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
28 0.14534265 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
29 0.09968585 0.00000000 0.26532042 0.06405872 0.00000000 0.00000000 0.00000000
30 0.08488686 0.04847908 0.22593193 0.01818293 0.00000000 0.01546079 0.00000000
31 0.00000000 0.29394268 0.34247265 0.05512419 0.02667153 0.00000000 0.00000000
32 0.52735633 0.06023489 0.14035934 0.00000000 0.02186218 0.01920992 0.00000000
33 0.13761771 0.23578138 0.36627855 0.05895597 0.00000000 0.02506488 0.00000000
34 0.00000000 0.33109737 0.00000000 0.16557853 0.08011426 0.00000000 0.00000000
35 0.21077671 0.24075014 0.28049801 0.18059516 0.08737997 0.00000000 0.00000000
36 0.00000000 0.00000000 0.00000000 0.45804827 0.22162413 0.19473727 0.03774470
37 0.00000000 0.42438121 0.00000000 0.31834329 0.23104296 0.00000000 0.02623254
38 0.00000000 0.25319763 0.00000000 0.56979737 0.00000000 0.00000000 0.03130213
39 0.00000000 0.00000000 0.42606753 0.27431828 0.06636369 0.23325050 0.00000000
40 0.00000000 0.30193945 0.35178968 0.16987156 0.10958856 0.04814678 0.01866397
41 0.00000000 0.00000000 0.00000000 0.39394265 0.12707132 0.33496608 0.04328291
14 15
7 0.00000000 0.000000e+00
8 0.00000000 0.000000e+00
9 0.00000000 0.000000e+00
10 0.00000000 0.000000e+00
11 0.00000000 0.000000e+00
12 0.00000000 0.000000e+00
13 0.00000000 0.000000e+00
14 0.00000000 0.000000e+00
15 0.00000000 0.000000e+00
16 0.00000000 0.000000e+00
17 0.00000000 0.000000e+00
18 0.00000000 0.000000e+00
19 0.00000000 0.000000e+00
20 0.00000000 0.000000e+00
21 0.00000000 0.000000e+00
22 0.00000000 0.000000e+00
23 0.00000000 0.000000e+00
24 0.00000000 0.000000e+00
25 0.00000000 0.000000e+00
26 0.00000000 0.000000e+00
27 0.00000000 0.000000e+00
28 0.00000000 0.000000e+00
29 0.00000000 0.000000e+00
30 0.00000000 0.000000e+00
31 0.00000000 0.000000e+00
32 0.00000000 0.000000e+00
33 0.00000000 0.000000e+00
34 0.00000000 0.000000e+00
35 0.00000000 0.000000e+00
36 0.08784563 0.000000e+00
37 0.00000000 0.000000e+00
38 0.14570287 0.000000e+00
39 0.00000000 0.000000e+00
40 0.00000000 0.000000e+00
41 0.10073507 1.971077e-06
Method: Kimura & Chikuni
Value
ConvergenceThreshold 1e-04
Iterations 10
Converged FALSE
0 1 2 3 4 5 6
7 0.6958245 0.3041755 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
8 0.6544066 0.3455934 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
9 0.6554390 0.3445610 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
10 0.6535474 0.3464526 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
11 0.7323008 0.2676992 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
12 0.6463002 0.3536998 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
13 0.5489010 0.4510990 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
14 0.4379660 0.5620340 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
15 0.6307655 0.3692345 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
16 0.3042060 0.6957940 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
17 0.4282697 0.5098471 0.06188322 0.0000000 0.00000000 0.00000000 0.0000000
18 0.0000000 0.9260433 0.07395668 0.0000000 0.00000000 0.00000000 0.0000000
19 0.1728280 0.4068622 0.29497487 0.1253350 0.00000000 0.00000000 0.0000000
20 0.0000000 0.5841476 0.41585244 0.0000000 0.00000000 0.00000000 0.0000000
21 0.0000000 0.2401840 0.42423728 0.3025934 0.03298536 0.00000000 0.0000000
22 0.0000000 0.2401095 0.42465284 0.3021573 0.03308036 0.00000000 0.0000000
23 0.0000000 0.0000000 0.24759146 0.4274716 0.06585827 0.00000000 0.2590787
24 0.0000000 0.0000000 0.00000000 0.7099853 0.11746927 0.12842475 0.0000000
25 0.0000000 0.0000000 0.18840720 0.6345497 0.11516888 0.06187422 0.0000000
26 0.0000000 0.0000000 0.00000000 0.5429432 0.17256431 0.13947130 0.0000000
27 0.0000000 0.0000000 0.00000000 0.7341563 0.17786593 0.07165312 0.0000000
28 0.0000000 0.0000000 0.00000000 0.2217697 0.05060747 0.41239861 0.2013143
29 0.0000000 0.0000000 0.00000000 0.2654165 0.05722138 0.18844562 0.0000000
30 0.0000000 0.0000000 0.00000000 0.0000000 0.05369700 0.08690413 0.4133656
31 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.3044864
32 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.2732066
33 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.14998883 0.0000000
34 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.5868292
35 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
36 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
37 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
38 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
39 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
40 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
41 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
7 8 9 10 11 12
7 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
8 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
9 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
10 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
11 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
12 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
13 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
14 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
15 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
16 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
17 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
18 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
19 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
20 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
21 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
22 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
23 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
24 0.04412072 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
25 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
26 0.00000000 0.00000000 0.1450212 0.000000000 0.00000000 0.000000e+00
27 0.00000000 0.01632467 0.0000000 0.000000000 0.00000000 0.000000e+00
28 0.11390994 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
29 0.06452729 0.00000000 0.4139431 0.010446083 0.00000000 0.000000e+00
30 0.06034916 0.01962399 0.3627066 0.003353524 0.00000000 2.026387e-10
31 0.00000000 0.10189439 0.5246796 0.008617451 0.06032216 0.000000e+00
32 0.40023076 0.02605364 0.2398674 0.000000000 0.06064158 2.691547e-10
33 0.10378674 0.10069475 0.6340828 0.011446921 0.00000000 3.456871e-10
34 0.00000000 0.14734101 0.0000000 0.033229564 0.23260024 0.000000e+00
35 0.15825645 0.10399561 0.4614528 0.035691828 0.24060327 0.000000e+00
36 0.00000000 0.00000000 0.0000000 0.066376088 0.48262668 1.995328e-09
37 0.00000000 0.20750251 0.0000000 0.071138344 0.72135903 0.000000e+00
38 0.00000000 0.10167557 0.0000000 0.105797535 0.00000000 0.000000e+00
39 0.00000000 0.00000000 0.6962935 0.074407486 0.22929899 4.534619e-09
40 0.00000000 0.15464452 0.4710289 0.041814034 0.33251249 8.519749e-10
41 0.00000000 0.00000000 0.0000000 0.084877699 0.34765438 5.174171e-09
13 14 15
7 0.000000e+00 0.0000000 0.000000e+00
8 0.000000e+00 0.0000000 0.000000e+00
9 0.000000e+00 0.0000000 0.000000e+00
10 0.000000e+00 0.0000000 0.000000e+00
11 0.000000e+00 0.0000000 0.000000e+00
12 0.000000e+00 0.0000000 0.000000e+00
13 0.000000e+00 0.0000000 0.000000e+00
14 0.000000e+00 0.0000000 0.000000e+00
15 0.000000e+00 0.0000000 0.000000e+00
16 0.000000e+00 0.0000000 0.000000e+00
17 0.000000e+00 0.0000000 0.000000e+00
18 0.000000e+00 0.0000000 0.000000e+00
19 0.000000e+00 0.0000000 0.000000e+00
20 0.000000e+00 0.0000000 0.000000e+00
21 0.000000e+00 0.0000000 0.000000e+00
22 0.000000e+00 0.0000000 0.000000e+00
23 0.000000e+00 0.0000000 0.000000e+00
24 0.000000e+00 0.0000000 0.000000e+00
25 0.000000e+00 0.0000000 0.000000e+00
26 0.000000e+00 0.0000000 0.000000e+00
27 0.000000e+00 0.0000000 0.000000e+00
28 0.000000e+00 0.0000000 0.000000e+00
29 0.000000e+00 0.0000000 0.000000e+00
30 0.000000e+00 0.0000000 0.000000e+00
31 0.000000e+00 0.0000000 0.000000e+00
32 0.000000e+00 0.0000000 0.000000e+00
33 0.000000e+00 0.0000000 0.000000e+00
34 0.000000e+00 0.0000000 0.000000e+00
35 0.000000e+00 0.0000000 0.000000e+00
36 1.098383e-07 0.4509971 0.000000e+00
37 1.183897e-07 0.0000000 0.000000e+00
38 1.176692e-07 0.7925268 0.000000e+00
39 0.000000e+00 0.0000000 0.000000e+00
40 9.379858e-08 0.0000000 0.000000e+00
41 1.898843e-07 0.5674677 4.063329e-97
Method: Hoenig & Heisey
Value
ConvergenceThreshold 1e-04
Iterations 245
Converged TRUE
0 1 2 3 4
7 9.999999e-01 8.509212e-08 9.980984e-10 8.205526e-15 4.059003e-16
8 9.999980e-01 1.977944e-06 1.092574e-08 9.269287e-14 6.574612e-15
9 9.999667e-01 3.320372e-05 1.080429e-07 1.012163e-12 1.032603e-13
10 9.995966e-01 4.024141e-04 9.648831e-07 1.068031e-11 1.572081e-12
11 9.964797e-01 3.512570e-03 7.763152e-06 1.086423e-10 2.314442e-11
12 9.781409e-01 2.180354e-02 5.556115e-05 1.051913e-09 3.253361e-10
13 9.072961e-01 9.236441e-02 3.394685e-04 9.303634e-09 4.190426e-09
14 7.473841e-01 2.509518e-01 1.664008e-03 7.063977e-08 4.647898e-08
15 5.519368e-01 4.414562e-01 6.606057e-03 4.648079e-07 4.481580e-07
16 4.108260e-01 5.652869e-01 2.387991e-02 2.979872e-06 4.223320e-06
17 3.372943e-01 5.766251e-01 8.601738e-02 2.036953e-05 4.256815e-05
18 2.819469e-01 4.325003e-01 2.849885e-01 1.370404e-04 4.235924e-04
19 1.774725e-01 1.764190e-01 6.423240e-01 6.711172e-04 3.077812e-03
20 7.463514e-02 3.472275e-02 8.737964e-01 2.122627e-03 1.448806e-02
21 2.650131e-02 4.167305e-03 9.066889e-01 5.479457e-03 5.583611e-02
22 8.636087e-03 3.314997e-04 7.800322e-01 1.254885e-02 1.915011e-01
23 2.147258e-03 1.453079e-05 4.625564e-01 2.119652e-02 4.859260e-01
24 3.346613e-04 2.883438e-07 1.553286e-01 2.169483e-02 7.494601e-01
25 3.758483e-05 2.977684e-09 3.395505e-02 1.546716e-02 8.076776e-01
26 3.636076e-06 1.913025e-11 5.776318e-03 9.182375e-03 7.270532e-01
27 3.031844e-07 7.650279e-14 7.651237e-04 4.541819e-03 5.469822e-01
28 1.949667e-08 1.704019e-16 7.061102e-05 1.674794e-03 3.077409e-01
29 8.871921e-10 1.939707e-19 4.165789e-06 4.224478e-04 1.188027e-01
30 2.980423e-11 1.177231e-22 1.639100e-07 7.604396e-05 3.283186e-02
31 8.012680e-13 4.129409e-26 4.662662e-09 1.058944e-05 7.040928e-03
32 1.761591e-14 8.554651e-30 9.798736e-11 1.165696e-06 1.197338e-03
33 3.082432e-16 1.018683e-33 1.480635e-12 9.872702e-08 1.571414e-04
34 4.198978e-18 6.820215e-38 1.573504e-14 6.292525e-09 1.556866e-05
35 4.534457e-20 2.614265e-42 1.197567e-16 3.073424e-10 1.185683e-06
36 4.045452e-22 5.978913e-47 6.802557e-19 1.198828e-11 7.233884e-08
37 3.079426e-24 8.425907e-52 2.978420e-21 3.856816e-13 3.651411e-09
38 2.026695e-26 7.414604e-57 1.018582e-23 1.037036e-14 1.545223e-10
39 1.152909e-28 4.072942e-62 2.720038e-26 2.329828e-16 5.480690e-12
40 5.634904e-31 1.388271e-67 5.637918e-29 4.347256e-18 1.619531e-13
41 2.353456e-33 2.920311e-73 9.021343e-32 6.700569e-20 3.965488e-15
5 6 7 8 9
7 5.359797e-18 6.402268e-21 2.020887e-18 6.298810e-21 9.615409e-25
8 6.323221e-17 1.634471e-19 1.779202e-17 4.574960e-20 2.366695e-23
9 7.587242e-16 4.045792e-18 1.655420e-16 3.621125e-19 5.938544e-22
10 9.256580e-15 9.706845e-17 1.627258e-15 3.122429e-18 1.518611e-20
11 1.145486e-13 2.251918e-15 1.685859e-14 2.926080e-17 3.948149e-19
12 1.419668e-12 4.987832e-14 1.817557e-13 2.942451e-16 1.030400e-17
13 1.691089e-11 1.012235e-12 1.956958e-12 3.047103e-15 2.590650e-16
14 1.819540e-10 1.768860e-11 1.977583e-11 3.053881e-14 5.897050e-15
15 1.785154e-09 2.686901e-10 1.893438e-10 2.990254e-13 1.226839e-13
16 1.795482e-08 3.988675e-09 1.931091e-09 3.216083e-12 2.622645e-12
17 2.025990e-07 6.332621e-08 2.295881e-08 4.157851e-11 6.304488e-11
18 2.367386e-06 9.925244e-07 2.937079e-07 5.964279e-10 1.573053e-09
19 2.118723e-05 1.135794e-05 2.990195e-06 7.020894e-09 3.013133e-08
20 1.288536e-04 8.419812e-05 2.149535e-05 6.017495e-08 3.931135e-07
21 6.729742e-04 5.109897e-04 1.378839e-04 4.745596e-07 4.414740e-06
22 3.280911e-03 2.759581e-03 8.578685e-04 3.743102e-06 4.638676e-05
23 1.241298e-02 1.102522e-02 4.303855e-03 2.454879e-05 3.791198e-04
24 2.994196e-02 2.677200e-02 1.430412e-02 1.099823e-04 1.980108e-03
25 5.293445e-02 4.542091e-02 3.620452e-02 3.869380e-04 7.597370e-03
26 8.199326e-02 6.436349e-02 8.342384e-02 1.277949e-03 2.559923e-02
27 1.113370e-01 7.622059e-02 1.750989e-01 3.964414e-03 7.579141e-02
28 1.185903e-01 6.749636e-02 2.995496e-01 1.033628e-02 1.764285e-01
29 9.091387e-02 4.100977e-02 3.832392e-01 2.078230e-02 2.962765e-01
30 5.233384e-02 1.783581e-02 3.825485e-01 3.361752e-02 3.744592e-01
31 2.452128e-02 6.019130e-03 3.229649e-01 4.742614e-02 3.861247e-01
32 9.556503e-03 1.610636e-03 2.356480e-01 5.962622e-02 3.319357e-01
33 3.014981e-03 3.325965e-04 1.446258e-01 6.502168e-02 2.315355e-01
34 7.531819e-04 5.184360e-05 7.303010e-02 6.015625e-02 1.281796e-01
35 1.517103e-04 6.211547e-06 3.089597e-02 4.808117e-02 5.734924e-02
36 2.567784e-05 5.961559e-07 1.141233e-02 3.459947e-02 2.161088e-02
37 3.771648e-06 4.733435e-08 3.801195e-03 2.315074e-02 7.083605e-03
38 4.871785e-07 3.150681e-09 1.156896e-03 1.459542e-02 2.046577e-03
39 5.532244e-08 1.757584e-10 3.216391e-04 8.667548e-03 5.210339e-04
40 5.489938e-09 8.167853e-12 8.119709e-05 4.819487e-03 1.161888e-04
41 4.735108e-10 3.145020e-13 1.851197e-05 2.495592e-03 2.257185e-05
10 11 12 13 14
7 3.482067e-21 2.024162e-23 1.413612e-25 2.501565e-25 2.166190e-26
8 2.209924e-20 1.787360e-22 1.749231e-24 1.321938e-24 1.894079e-25
9 1.549896e-19 1.732162e-21 2.338621e-23 7.906673e-24 1.842985e-24
10 1.200821e-18 1.841792e-20 3.377024e-22 5.350879e-23 1.994957e-23
11 1.025313e-17 2.143480e-19 5.254379e-21 4.087490e-22 2.396539e-22
12 9.526249e-17 2.695940e-18 8.697742e-20 3.479955e-21 3.154713e-21
13 9.242720e-16 3.516722e-17 1.469992e-18 3.168845e-20 4.367016e-20
14 8.800810e-15 4.471320e-16 2.383851e-17 2.900491e-19 5.974367e-19
15 8.302218e-14 5.593796e-15 3.744575e-16 2.693945e-18 8.154264e-18
16 8.723414e-13 7.741465e-14 6.405567e-15 2.854466e-17 1.248348e-16
17 1.117273e-11 1.297014e-12 1.305882e-13 3.776065e-16 2.345871e-15
18 1.610041e-10 2.428265e-11 2.928639e-12 5.756482e-15 4.994762e-14
19 1.930714e-09 3.757294e-10 5.343696e-11 7.479560e-14 8.911805e-13
20 1.709407e-08 4.263102e-09 7.038418e-10 7.349194e-13 1.182226e-11
21 1.412156e-07 4.482397e-08 8.457236e-09 6.900980e-12 1.473607e-10
22 1.183159e-06 4.747262e-07 1.007665e-07 6.731370e-11 1.875961e-09
23 8.358322e-06 4.210330e-06 9.897603e-07 5.670347e-10 2.027767e-08
24 4.090223e-05 2.569010e-05 6.584254e-06 3.388955e-09 1.528980e-07
25 1.593891e-04 1.239720e-04 3.410182e-05 1.651976e-08 9.244984e-07
26 5.912638e-04 5.656105e-04 1.643881e-04 7.851466e-08 5.358693e-06
27 2.089081e-03 2.441109e-03 7.379471e-04 3.640385e-07 2.979202e-05
28 6.290817e-03 8.917833e-03 2.760378e-03 1.473396e-06 1.421530e-04
29 1.481358e-02 2.530215e-02 7.894486e-03 4.776294e-06 5.341342e-04
30 2.845863e-02 5.816761e-02 1.800905e-02 1.293783e-05 1.648856e-03
31 4.835100e-02 1.174538e-01 3.552271e-02 3.174445e-05 4.533045e-03
32 7.423728e-02 2.128644e-01 6.190950e-02 7.209367e-05 1.134121e-02
33 1.002531e-01 3.369945e-01 9.278513e-02 1.474972e-04 2.513190e-02
34 1.164751e-01 4.558549e-01 1.169687e-01 2.659058e-04 4.824892e-02
35 1.185490e-01 5.365183e-01 1.262993e-01 4.301297e-04 8.171778e-02
36 1.101591e-01 5.725654e-01 1.217310e-01 6.506194e-04 1.272449e-01
37 9.651653e-02 5.722017e-01 1.081610e-01 9.504110e-04 1.881310e-01
38 8.079731e-02 5.426398e-01 8.977695e-02 1.358651e-03 2.676279e-01
39 6.460678e-02 4.881855e-01 6.959142e-02 1.900151e-03 3.662059e-01
40 4.905030e-02 4.141572e-01 5.007717e-02 2.584336e-03 4.791141e-01
41 3.516668e-02 3.295310e-01 3.327060e-02 3.399648e-03 5.960953e-01
15
7 6.066447e-93
8 2.558161e-92
9 1.244987e-91
10 6.990547e-91
11 4.517707e-90
12 3.317956e-89
13 2.657628e-88
14 2.181831e-87
15 1.853340e-86
16 1.831338e-85
17 2.303672e-84
18 3.405151e-83
19 4.374351e-82
20 4.333073e-81
21 4.182599e-80
22 4.276403e-79
23 3.850212e-78
24 2.507848e-77
25 1.358500e-76
26 7.316241e-76
27 3.919458e-75
28 1.868960e-74
29 7.278367e-74
30 2.415055e-73
31 7.401443e-73
32 2.140865e-72
33 5.688264e-72
34 1.357963e-71
35 2.966089e-71
36 6.177273e-71
37 1.266854e-70
38 2.592560e-70
39 5.292675e-70
40 1.071427e-69
41 2.139118e-69
Method: Gascuel
Value
ConvergenceThreshold 1e-04
alpha 0.112751
beta 0.07044978
gamma 0.05807639
Converged TRUE
ALKr documentation built on May 30, 2017, 7:42 a.m.
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Description Usage Arguments Details Value References See Also Examples
Description
Generation of Age-Length Keys (ALK) using incomplete data, by methods based on inverse ALKs.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 | gascuel(x, fi1, fi2, initial_values, threshold = 1e-04, maxiter = 2000,
age_classes = colnames(x), length_classes = rownames(x), name = "",
description = "")
hoenig_heisey(x, fi1, fi2, threshold = 1e-04, maxiter = 2000,
age_classes = colnames(x), length_classes = rownames(x), name = "",
description = "")
inverse_ALK(x, fi1, fi2, age_classes = colnames(x),
length_classes = rownames(x), name = "", description = "")
kimura_chikuni(x, fi1, fi2, threshold = 1e-04, maxiter = 2000,
age_classes = colnames(x), length_classes = rownames(x), name = "",
description = "")
|
Arguments
x |
A i \times j matrix with |
fi1 |
A vector of length |
fi2 |
A vector of length |
age_classes |
A vector with the name of each age class. |
length_classes |
A vector with the name of each age class. |
threshold |
The value at which convergence is considered to be achieved: see ‘details’. |
maxiter |
The maximum number of iterations of the EM algorithm: see ‘details’. |
initial_values |
A vector with the initial values for α, β and γ: see ‘details’. |
name |
A string with the name of the ALK. |
description |
A string describing the ALK. |
Details
inverseALK calculates an ALK from a sample of
aged-fish, the length distribution of the sampled
population and the length distribution of a population with
unknown age-length data, as described by Clark (1981),
Bartoo and Parker (1983) and Hilborn and Walters (1992).
kimura_chikuni, hoenig_heisey and
gascuel use the same inputs as inverseALK to
calculate an ALK as described respectively by Kimura and
Chikuni (1987), Hoenig and Heisey (1987) and Gascuel
(1994).
hoenig employs the generalized method proposed by
Hoenig et al. (1993, 1994), which takes an undefined
number of data sets with known and unknown age information
and combines them to calculate the ALK.
The returned ALKr object contains information on the
convergence threshold that was used, the number of
iterations ran, and if convergence was reached.
Initial values
The method proposed by Gascuel (1994) is based on the assumption that the length distribution within each age class follows a Normal distribution, where the standard deviation of length at age σ(j) is given by a linear model as a function of three parameters α, β and γ:
σ(j) = α + β l(j) + γ Δl(j)
where Δl(j) is the difference
between the mean lengths at age-class j and
age-class j-1.
Convergence
The methods proposed by Kimura and Chikuni (1987), Hoenig and Heisey (1987) and Gascuel (1994) are all based on the EM algorithm as defined by Dempster et al. (1997), and build the ALK by a series of iterations which are repeated until convergence is acheived.
The convergence is tested by evaluating the sum of the
absolute differences between the ages distributions
calculated on the previous and current iterations:
sum(abs(pj_prev - pj_curr)). The algorithm exits
when either this value is smaller than the specified
threshold or when the number of iterations reaches
maxiter.
Value
An ALKr object, containing a i \times j matrix
with the probability of an individual of length i
having age j, i.e. P(j|i), a i \times j
matrix with the estimated number of individuals of length
i and age j, and information about the method
used to generate the key.
References
Bartoo, N.W., Parker, K.R. (1983). Stochastic age-frequency estimation using the von Bertalanffy growth equation. Fishery Bulletin, 81/1, 91-96
Clark, W.G. (1981). Restricted Least-Squares Estimates of
Age Composition from Length Composition. Canadian
Journal of Fisheries and Aquatic Sciences, 38/3,
297-307. DOI: 10.1139/f81-041
Dempster, A.P., Laird, N.M., Rubin, D.B. (1977). Maximum
Likelihood from Incomplete Data via the EM Algorithm.
Journal of the Royal Statistical Society. Series B
(Methodological), 39/1, 1-38. DOI:
10.2307/2984875
Gascuel, D. (1994). Une methode simple d'ajustement des
cles taille/age: application aux captures d'albacores
(Thunnus albacares) de l'Atlantique Est. Canadian
Journal of Fisheries and Aquatic Sciences, 51/3,
723-733. DOI: 10.1139/f94-072
Hilborn, R., Walters, C.J. (1992). Quantitative fisheries
stock assessment: Choice, dynamics and uncertainty.
Reviews in Fish Biology and Fisheries, 2/2,
177-178. DOI: 10.1007/BF00042883
Hoenig, J.M., Heisey, D.M. (1987), Use of a Log-Linear
Model with the EM Algorithm to Correct Estimates of Stock
Composition and to Convert Length to Age.
Transactions of the American Fisheries Society,
116/2, 232-243. DOI:
10.1577/1548-8659(1987)116<232:UOALMW>2.0.CO;2
See Also
hoenig
Examples
1 2 3 4 5 6 7 8 9 10 11 | data(hom)
inverse_ALK(hom$otoliths[[1]], fi1 = hom$F1992, fi2 = hom$F1993)
kimura_chikuni(hom$otoliths[[1]], fi1 = hom$F1992, fi2 = hom$F1993) # converges
kimura_chikuni(hom$otoliths[[1]], fi1 = hom$F1992, fi2 = hom$F1993, maxiter = 10) # won't converge
hoenig_heisey(hom$otoliths[[1]], fi1 = hom$F1992, fi2 = hom$F1993)
gascuel(hom$otoliths[[1]], fi1 = hom$F1992, fi2 = hom$F1993,
initial_values = c(0.1, 0.07, 0.06))
|
Example output
0 1 2 3 4
7 2.153102e+00 -1.171167e+00 1.871984e-02 -6.000848e-02 9.213687e-02
8 2.153102e+00 -1.171167e+00 1.871984e-02 -6.000848e-02 9.213687e-02
9 2.153102e+00 -1.171167e+00 1.871984e-02 -6.000848e-02 9.213687e-02
10 2.153102e+00 -1.171167e+00 1.871984e-02 -6.000848e-02 9.213687e-02
11 2.910497e+00 -2.132581e+00 3.702986e-01 -4.483765e-01 3.236365e-01
12 2.153102e+00 -1.171167e+00 1.871984e-02 -6.000848e-02 9.213687e-02
13 1.281385e+00 -6.463817e-02 -3.859263e-01 3.869799e-01 -1.743053e-01
14 2.673509e-01 1.222545e+00 -8.566356e-01 9.069443e-01 -4.842473e-01
15 2.153102e+00 -1.171167e+00 1.871984e-02 -6.000848e-02 9.213687e-02
16 -9.269517e-01 2.738555e+00 -1.411024e+00 1.519345e+00 -8.492887e-01
17 7.553016e-01 -2.648790e-01 1.121070e+00 -1.756179e+00 1.132965e+00
18 -2.165319e+00 3.246670e+00 1.603356e-01 -8.028364e-01 5.714089e-01
19 -1.321321e-02 7.828098e-02 -1.426248e-01 5.236309e+00 -4.981494e+00
20 2.490383e-01 -1.152376e+00 3.973004e+00 -5.749964e+00 3.566070e+00
21 5.664107e-02 -2.270293e-01 4.891580e-01 2.601567e-01 1.571723e+00
22 5.664107e-02 -2.270293e-01 4.891580e-01 2.601567e-01 1.571723e+00
23 -1.044458e-02 3.939251e-02 -8.940532e-02 -5.394977e-04 5.397472e-01
24 -5.374615e-02 1.553492e-01 -3.558837e-01 4.117349e-01 6.462598e-01
25 -3.976376e-02 1.332669e-01 -3.788722e-01 5.623755e-01 1.108979e+00
26 1.910224e-02 -3.399418e-02 1.133496e-01 -5.184960e-01 8.117601e-01
27 3.189523e-02 -3.377642e-02 1.655256e-01 -1.216013e+00 2.458940e+00
28 7.916112e-02 -2.717065e-01 5.994854e-01 -1.250691e-01 -2.931454e+00
29 3.884537e-04 8.293789e-03 -1.442592e-02 -1.060558e-01 4.286798e-01
30 2.792673e-03 -1.644396e-02 5.432607e-02 -4.492304e-02 -3.653887e-01
31 -3.086370e-02 5.572475e-02 -1.758505e-01 7.804397e-01 -1.252220e+00
32 1.609508e-02 -2.162789e-02 6.072914e-02 -3.907492e-01 9.497298e-01
33 4.754402e-03 -1.331637e-02 9.361678e-03 7.758777e-02 -9.266141e-02
34 1.787657e-02 -4.247241e-02 1.262201e-01 -3.735553e-01 2.714560e-01
35 -8.023094e-04 8.321309e-03 -1.573987e-02 -6.182394e-02 2.869240e-01
36 -1.113901e-02 2.525294e-02 -6.724159e-02 1.947889e-01 -2.011294e-01
37 1.113778e-02 -2.531674e-02 6.777310e-02 -1.963659e-01 1.991232e-01
38 2.404930e-02 -5.452150e-02 1.451757e-01 -4.205525e-01 4.342416e-01
39 -1.601102e-02 4.610215e-02 -1.047601e-01 1.193672e-01 1.868230e-01
40 1.057759e-03 -1.760813e-03 1.227977e-03 -3.200823e-03 3.808406e-02
41 3.812377e-16 -2.088106e-17 1.271024e-16 6.528252e-16 2.592327e-16
5 6 7 8 9
7 -3.469562e-02 -8.209329e-03 1.616737e-02 -1.799939e-04 -1.466226e-02
8 -3.469562e-02 -8.209329e-03 1.616737e-02 -1.799938e-04 -1.466226e-02
9 -3.469562e-02 -8.209329e-03 1.616737e-02 -1.799938e-04 -1.466226e-02
10 -3.469562e-02 -8.209329e-03 1.616737e-02 -1.799938e-04 -1.466226e-02
11 -2.508478e-02 -8.375689e-03 3.913545e-02 1.693911e-02 -5.715149e-02
12 -3.469562e-02 -8.209329e-03 1.616737e-02 -1.799938e-04 -1.466226e-02
13 -4.575712e-02 -8.017858e-03 -1.026751e-02 -1.988306e-02 3.424030e-02
14 -5.862455e-02 -7.795127e-03 -4.101820e-02 -4.280288e-02 9.112677e-02
15 -3.469562e-02 -8.209329e-03 1.616737e-02 -1.799938e-04 -1.466226e-02
16 -7.377946e-02 -7.532800e-03 -7.723553e-02 -6.979722e-02 1.581261e-01
17 -3.114932e-03 1.944843e-02 1.120191e-01 6.742831e-02 -2.107035e-01
18 -2.905152e-02 2.625918e-02 5.463255e-02 2.379077e-02 -1.087657e-01
19 9.924653e-01 2.148380e-03 -6.342199e-01 -9.077433e-02 8.912780e-01
20 7.739616e-02 6.777226e-02 3.403501e-01 2.308546e-01 -6.661022e-01
21 -1.153014e+00 -3.938947e-01 4.199205e-01 -7.319027e-02 -1.924432e-01
22 -1.153014e+00 -3.938947e-01 4.199205e-01 -7.319027e-02 -1.924432e-01
23 -5.325783e-01 1.514622e+00 4.816369e-02 -2.133375e-01 -1.886750e-01
24 8.239541e-02 -2.574033e-01 8.949490e-01 2.267711e-01 -6.856820e-01
25 6.545322e-01 -3.279034e-01 -9.194233e-01 -3.154256e-01 -6.313376e-01
26 1.313052e+00 -1.674162e-01 -1.563312e+00 -1.479172e+00 3.335860e+00
27 -3.719829e-01 -3.331450e-01 2.154869e-01 2.181180e+00 -1.445095e+00
28 3.962141e+00 7.752535e-01 -3.990457e-01 3.836618e-01 -8.818640e-01
29 -9.062469e-01 -8.805334e-02 1.043095e+00 -9.657711e-01 6.452537e-01
30 4.515309e-01 2.821212e-01 -5.318873e-01 -1.190236e-02 5.423833e-01
31 1.299040e-01 1.567422e-01 -1.457354e-01 1.765382e+00 1.394709e+00
32 -2.369568e+00 -1.714453e-01 2.819620e+00 -4.118617e-01 1.169238e+00
33 -3.445830e-02 -1.498705e-01 1.417848e-01 1.774666e+00 -8.023840e-01
34 8.090756e-01 6.056544e-02 -8.510558e-01 -1.623424e-01 -1.392939e+00
35 1.363288e-01 -1.113920e-01 -3.290942e-01 -1.101204e+00 -9.487247e-02
36 5.302499e-01 -2.267010e-02 -6.408978e-01 -5.197730e-01 -1.155242e-01
37 -4.895318e-01 2.401971e-02 5.988359e-01 4.425034e-01 1.087738e-01
38 -1.144818e+00 4.894512e-02 1.383709e+00 1.122198e+00 2.494186e-01
39 1.833874e+00 -2.020683e-01 -2.406054e+00 -1.438512e+00 -2.302220e+00
40 -4.394383e-01 -1.078606e-02 4.626880e-01 7.882276e-01 7.544497e-02
41 -3.881986e-16 8.162052e-17 2.168574e-16 -1.908484e-16 -8.826761e-17
10 11 12 13 14
7 2.294124e-02 -1.241020e-02 -1.068623e-04 1.963470e-03 -3.611497e-03
8 2.294124e-02 -1.241020e-02 -1.068623e-04 1.963470e-03 -3.611497e-03
9 2.294124e-02 -1.241020e-02 -1.068623e-04 1.963470e-03 -3.611497e-03
10 2.294124e-02 -1.241020e-02 -1.068623e-04 1.963470e-03 -3.611497e-03
11 5.258484e-02 -3.584594e-02 -4.873167e-03 7.624506e-03 -8.596809e-03
12 2.294124e-02 -1.241020e-02 -1.068623e-04 1.963470e-03 -3.611497e-03
13 -1.117678e-02 1.456294e-02 5.378870e-03 -4.552044e-03 2.126299e-03
14 -5.086495e-02 4.593976e-02 1.176021e-02 -1.213129e-02 8.800855e-03
15 2.294124e-02 -1.241020e-02 -1.068623e-04 1.963470e-03 -3.611497e-03
16 -9.760862e-02 8.289454e-02 1.927598e-02 -2.105793e-02 1.666197e-02
17 1.648024e-01 -1.171426e-01 -2.109680e-02 2.623911e-02 -2.685163e-02
18 9.483081e-02 -6.015040e-02 -9.435883e-03 1.224157e-02 -1.494492e-02
19 -1.027909e+00 5.873391e-01 4.766471e-02 -1.038030e-01 1.607052e-01
20 4.914915e-01 -3.623367e-01 -7.041685e-02 8.366375e-02 -8.070431e-02
21 5.308087e-01 -2.634704e-01 2.469743e-02 3.404658e-02 -8.384691e-02
22 5.308087e-01 -2.634704e-01 2.469743e-02 3.404658e-02 -8.384691e-02
23 3.336002e-01 -2.545456e-01 -2.883656e-01 1.540107e-01 -5.845855e-02
24 5.118745e-01 -4.942222e-01 -1.538098e-01 1.704648e-01 -1.026555e-01
25 3.472362e-01 5.481309e-01 7.434065e-01 -4.918682e-01 2.191440e-02
26 -3.249965e+00 2.634034e+00 -3.403546e-01 -5.202724e-01 6.372868e-01
27 6.087261e-01 -1.644167e+00 1.512233e-01 4.954144e-01 -2.575280e-01
28 -5.726294e-01 3.075842e-01 7.632936e-02 -1.000023e-01 9.963826e-02
29 3.377810e+00 -1.600943e+00 -7.898843e-01 4.143631e-01 -4.695168e-01
30 -8.486844e-02 -3.829242e-01 1.360392e+00 -4.614107e-02 -1.692309e-01
31 -1.640447e+00 5.756066e-01 -1.040557e+00 2.922549e-02 3.680798e-01
32 -1.851554e+00 1.295082e+00 -2.187204e-01 -2.238582e-01 3.436302e-01
33 1.274128e+00 -2.193410e+00 9.825934e-01 5.298159e-01 -4.775364e-01
34 1.497087e+00 1.651714e+00 4.950962e-01 -1.328737e+00 2.162862e-01
35 8.957068e-01 2.437406e+00 -4.811562e-02 -1.417536e+00 3.954476e-01
36 -2.220930e-01 7.467712e-01 8.023514e-01 1.986511e-01 3.777181e-01
37 2.059248e-01 -6.008317e-01 -7.949488e-01 3.233452e+00 -1.760936e+00
38 4.795025e-01 -1.612291e+00 -1.732290e+00 -4.288910e-01 2.566882e+00
39 2.286890e+00 1.099319e+00 3.988292e+00 -1.743236e+00 -2.552721e-01
40 1.755745e-01 -1.466669e+00 -1.461826e-01 3.509426e+00 -1.937718e+00
41 -2.215838e-18 -1.782157e-17 -5.963917e-17 2.057545e-16 5.164343e-16
15
7 2.119375e-05
8 2.119375e-05
9 2.119375e-05
10 2.119375e-05
11 1.693613e-04
12 2.119375e-05
13 -1.493382e-04
14 -3.477115e-04
15 2.119375e-05
16 -5.813502e-04
17 6.928061e-04
18 3.346198e-04
19 -2.151416e-03
20 2.259677e-03
21 -2.626250e-04
22 -2.626250e-04
23 6.813558e-03
24 3.604001e-03
25 -1.524768e-02
26 8.536757e-03
27 -6.683569e-03
28 -1.483631e-03
29 2.301299e-02
30 -3.983675e-02
31 2.986030e-02
32 5.259866e-03
33 -3.105504e-02
34 5.725726e-03
35 2.044579e-02
36 -7.531552e-02
37 -2.361285e-02
38 -6.075735e-02
39 -9.253340e-02
40 -4.597605e-02
41 1.000000e+00
Method: Classic Inverse ALK
0 1 2 3 4 5 6
7 0.6304005 0.3695995 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
8 0.6304005 0.3695995 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
9 0.6304005 0.3695995 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
10 0.6304005 0.3695995 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
11 0.7189785 0.2810215 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
12 0.6304005 0.3695995 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
13 0.5320734 0.4679266 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
14 0.4222942 0.5777058 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
15 0.6304005 0.3695995 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
16 0.2989382 0.7010618 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
17 0.4333541 0.5081451 0.05850078 0.0000000 0.00000000 0.00000000 0.0000000
18 0.0000000 0.9287200 0.07127996 0.0000000 0.00000000 0.00000000 0.0000000
19 0.1758596 0.4124212 0.28488273 0.1268365 0.00000000 0.00000000 0.0000000
20 0.0000000 0.5914511 0.40854886 0.0000000 0.00000000 0.00000000 0.0000000
21 0.0000000 0.2435485 0.42058195 0.2996047 0.03626485 0.00000000 0.0000000
22 0.0000000 0.2435485 0.42058195 0.2996047 0.03626485 0.00000000 0.0000000
23 0.0000000 0.0000000 0.24176235 0.4305530 0.06948686 0.00000000 0.2581978
24 0.0000000 0.0000000 0.00000000 0.6981634 0.12676100 0.12537196 0.0000000
25 0.0000000 0.0000000 0.18088809 0.6442849 0.11697862 0.05784839 0.0000000
26 0.0000000 0.0000000 0.00000000 0.5539899 0.17881663 0.13264288 0.0000000
27 0.0000000 0.0000000 0.00000000 0.7364744 0.17828917 0.06612581 0.0000000
28 0.0000000 0.0000000 0.00000000 0.2218824 0.05371432 0.39844289 0.1995905
29 0.0000000 0.0000000 0.00000000 0.2575943 0.06235963 0.18502890 0.0000000
30 0.0000000 0.0000000 0.00000000 0.0000000 0.05622025 0.08340629 0.4178040
31 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.2973865
32 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.2735107
33 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.14182476 0.0000000
34 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.5240278
35 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
36 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
37 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
38 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
39 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
40 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
41 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
7 8 9 10 11 12
7 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
8 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
9 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
10 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
11 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
12 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
13 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
14 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
15 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
16 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
17 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
18 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
19 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
20 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
21 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
22 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
23 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
24 0.04970363 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
25 0.00000000 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
26 0.00000000 0.00000000 0.1345506 0.00000000 0.00000000 0.000000e+00
27 0.00000000 0.01911062 0.0000000 0.00000000 0.00000000 0.000000e+00
28 0.12636994 0.00000000 0.0000000 0.00000000 0.00000000 0.000000e+00
29 0.07335459 0.00000000 0.3753800 0.04628254 0.00000000 0.000000e+00
30 0.06613273 0.02410475 0.3384234 0.01390866 0.00000000 3.816275e-09
31 0.00000000 0.13725913 0.4817692 0.03959987 0.04398538 0.000000e+00
32 0.43293049 0.03155980 0.2215450 0.00000000 0.04045399 4.996564e-09
33 0.11245267 0.12296377 0.5754580 0.04730080 0.00000000 6.489228e-09
34 0.00000000 0.18139931 0.0000000 0.13955870 0.15501420 0.000000e+00
35 0.16492593 0.12022785 0.4219906 0.13874509 0.15411048 0.000000e+00
36 0.00000000 0.00000000 0.0000000 0.32258845 0.35831365 4.425612e-08
37 0.00000000 0.24526931 0.0000000 0.28304518 0.47158671 0.000000e+00
38 0.00000000 0.11077422 0.0000000 0.38350631 0.00000000 0.000000e+00
39 0.00000000 0.00000000 0.6616441 0.21754006 0.12081581 5.968893e-08
40 0.00000000 0.15020291 0.5272008 0.13000264 0.19253311 1.189010e-08
41 0.00000000 0.00000000 0.0000000 0.32686114 0.24203969 8.968459e-08
13 14 15
7 0.000000e+00 0.0000000 0.000000e+00
8 0.000000e+00 0.0000000 0.000000e+00
9 0.000000e+00 0.0000000 0.000000e+00
10 0.000000e+00 0.0000000 0.000000e+00
11 0.000000e+00 0.0000000 0.000000e+00
12 0.000000e+00 0.0000000 0.000000e+00
13 0.000000e+00 0.0000000 0.000000e+00
14 0.000000e+00 0.0000000 0.000000e+00
15 0.000000e+00 0.0000000 0.000000e+00
16 0.000000e+00 0.0000000 0.000000e+00
17 0.000000e+00 0.0000000 0.000000e+00
18 0.000000e+00 0.0000000 0.000000e+00
19 0.000000e+00 0.0000000 0.000000e+00
20 0.000000e+00 0.0000000 0.000000e+00
21 0.000000e+00 0.0000000 0.000000e+00
22 0.000000e+00 0.0000000 0.000000e+00
23 0.000000e+00 0.0000000 0.000000e+00
24 0.000000e+00 0.0000000 0.000000e+00
25 0.000000e+00 0.0000000 0.000000e+00
26 0.000000e+00 0.0000000 0.000000e+00
27 0.000000e+00 0.0000000 0.000000e+00
28 0.000000e+00 0.0000000 0.000000e+00
29 0.000000e+00 0.0000000 0.000000e+00
30 0.000000e+00 0.0000000 0.000000e+00
31 0.000000e+00 0.0000000 0.000000e+00
32 0.000000e+00 0.0000000 0.000000e+00
33 0.000000e+00 0.0000000 0.000000e+00
34 0.000000e+00 0.0000000 0.000000e+00
35 0.000000e+00 0.0000000 0.000000e+00
36 1.126047e-04 0.3189852 0.000000e+00
37 9.880152e-05 0.0000000 0.000000e+00
38 8.924608e-05 0.5056302 0.000000e+00
39 0.000000e+00 0.0000000 0.000000e+00
40 6.050605e-05 0.0000000 0.000000e+00
41 1.521283e-04 0.4309470 7.983815e-83
Method: Kimura & Chikuni
Value
ConvergenceThreshold 1e-04
Iterations 193
Converged TRUE
0 1 2 3 4 5 6
7 0.6763306 0.3236694 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
8 0.6763306 0.3236694 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
9 0.6763306 0.3236694 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
10 0.6763306 0.3236694 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
11 0.7581245 0.2418755 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
12 0.6763306 0.3236694 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
13 0.5821229 0.4178771 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
14 0.4724433 0.5275567 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
15 0.6763306 0.3236694 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
16 0.3431394 0.6568606 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
17 0.4728580 0.4525883 0.07455370 0.00000000 0.00000000 0.00000000 0.0000000
18 0.0000000 0.9010484 0.09895157 0.00000000 0.00000000 0.00000000 0.0000000
19 0.1920689 0.3676712 0.36339315 0.07686671 0.00000000 0.00000000 0.0000000
20 0.0000000 0.5029259 0.49707407 0.00000000 0.00000000 0.00000000 0.0000000
21 0.0000000 0.2137092 0.52805636 0.17871534 0.07951912 0.00000000 0.0000000
22 0.0000000 0.2137092 0.52805636 0.17871534 0.07951912 0.00000000 0.0000000
23 0.0000000 0.0000000 0.32408177 0.27420549 0.16267643 0.00000000 0.2390363
24 0.0000000 0.0000000 0.00000000 0.45471805 0.30348917 0.17391525 0.0000000
25 0.0000000 0.0000000 0.24124182 0.40822928 0.27246151 0.07806739 0.0000000
26 0.0000000 0.0000000 0.00000000 0.33768323 0.40067106 0.17220419 0.0000000
27 0.0000000 0.0000000 0.00000000 0.46159915 0.41077570 0.08827353 0.0000000
28 0.0000000 0.0000000 0.00000000 0.12170805 0.10830763 0.46549474 0.1591469
29 0.0000000 0.0000000 0.00000000 0.16695127 0.14856944 0.25541430 0.0000000
30 0.0000000 0.0000000 0.00000000 0.00000000 0.12651337 0.10874822 0.3717968
31 0.0000000 0.0000000 0.00000000 0.00000000 0.00000000 0.00000000 0.2817889
32 0.0000000 0.0000000 0.00000000 0.00000000 0.00000000 0.00000000 0.2309773
33 0.0000000 0.0000000 0.00000000 0.00000000 0.00000000 0.17630151 0.0000000
34 0.0000000 0.0000000 0.00000000 0.00000000 0.00000000 0.00000000 0.4232098
35 0.0000000 0.0000000 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
36 0.0000000 0.0000000 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
37 0.0000000 0.0000000 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
38 0.0000000 0.0000000 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
39 0.0000000 0.0000000 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
40 0.0000000 0.0000000 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
41 0.0000000 0.0000000 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000
7 8 9 10 11 12 13
7 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
8 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
9 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
10 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
11 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
12 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
13 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
14 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
15 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
16 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
17 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
18 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
19 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
20 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
21 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
22 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
23 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
24 0.06787752 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
25 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
26 0.00000000 0.00000000 0.08944152 0.00000000 0.00000000 0.00000000 0.00000000
27 0.00000000 0.03935163 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
28 0.14534265 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
29 0.09968585 0.00000000 0.26532042 0.06405872 0.00000000 0.00000000 0.00000000
30 0.08488686 0.04847908 0.22593193 0.01818293 0.00000000 0.01546079 0.00000000
31 0.00000000 0.29394268 0.34247265 0.05512419 0.02667153 0.00000000 0.00000000
32 0.52735633 0.06023489 0.14035934 0.00000000 0.02186218 0.01920992 0.00000000
33 0.13761771 0.23578138 0.36627855 0.05895597 0.00000000 0.02506488 0.00000000
34 0.00000000 0.33109737 0.00000000 0.16557853 0.08011426 0.00000000 0.00000000
35 0.21077671 0.24075014 0.28049801 0.18059516 0.08737997 0.00000000 0.00000000
36 0.00000000 0.00000000 0.00000000 0.45804827 0.22162413 0.19473727 0.03774470
37 0.00000000 0.42438121 0.00000000 0.31834329 0.23104296 0.00000000 0.02623254
38 0.00000000 0.25319763 0.00000000 0.56979737 0.00000000 0.00000000 0.03130213
39 0.00000000 0.00000000 0.42606753 0.27431828 0.06636369 0.23325050 0.00000000
40 0.00000000 0.30193945 0.35178968 0.16987156 0.10958856 0.04814678 0.01866397
41 0.00000000 0.00000000 0.00000000 0.39394265 0.12707132 0.33496608 0.04328291
14 15
7 0.00000000 0.000000e+00
8 0.00000000 0.000000e+00
9 0.00000000 0.000000e+00
10 0.00000000 0.000000e+00
11 0.00000000 0.000000e+00
12 0.00000000 0.000000e+00
13 0.00000000 0.000000e+00
14 0.00000000 0.000000e+00
15 0.00000000 0.000000e+00
16 0.00000000 0.000000e+00
17 0.00000000 0.000000e+00
18 0.00000000 0.000000e+00
19 0.00000000 0.000000e+00
20 0.00000000 0.000000e+00
21 0.00000000 0.000000e+00
22 0.00000000 0.000000e+00
23 0.00000000 0.000000e+00
24 0.00000000 0.000000e+00
25 0.00000000 0.000000e+00
26 0.00000000 0.000000e+00
27 0.00000000 0.000000e+00
28 0.00000000 0.000000e+00
29 0.00000000 0.000000e+00
30 0.00000000 0.000000e+00
31 0.00000000 0.000000e+00
32 0.00000000 0.000000e+00
33 0.00000000 0.000000e+00
34 0.00000000 0.000000e+00
35 0.00000000 0.000000e+00
36 0.08784563 0.000000e+00
37 0.00000000 0.000000e+00
38 0.14570287 0.000000e+00
39 0.00000000 0.000000e+00
40 0.00000000 0.000000e+00
41 0.10073507 1.971077e-06
Method: Kimura & Chikuni
Value
ConvergenceThreshold 1e-04
Iterations 10
Converged FALSE
0 1 2 3 4 5 6
7 0.6958245 0.3041755 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
8 0.6544066 0.3455934 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
9 0.6554390 0.3445610 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
10 0.6535474 0.3464526 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
11 0.7323008 0.2676992 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
12 0.6463002 0.3536998 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
13 0.5489010 0.4510990 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
14 0.4379660 0.5620340 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
15 0.6307655 0.3692345 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
16 0.3042060 0.6957940 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
17 0.4282697 0.5098471 0.06188322 0.0000000 0.00000000 0.00000000 0.0000000
18 0.0000000 0.9260433 0.07395668 0.0000000 0.00000000 0.00000000 0.0000000
19 0.1728280 0.4068622 0.29497487 0.1253350 0.00000000 0.00000000 0.0000000
20 0.0000000 0.5841476 0.41585244 0.0000000 0.00000000 0.00000000 0.0000000
21 0.0000000 0.2401840 0.42423728 0.3025934 0.03298536 0.00000000 0.0000000
22 0.0000000 0.2401095 0.42465284 0.3021573 0.03308036 0.00000000 0.0000000
23 0.0000000 0.0000000 0.24759146 0.4274716 0.06585827 0.00000000 0.2590787
24 0.0000000 0.0000000 0.00000000 0.7099853 0.11746927 0.12842475 0.0000000
25 0.0000000 0.0000000 0.18840720 0.6345497 0.11516888 0.06187422 0.0000000
26 0.0000000 0.0000000 0.00000000 0.5429432 0.17256431 0.13947130 0.0000000
27 0.0000000 0.0000000 0.00000000 0.7341563 0.17786593 0.07165312 0.0000000
28 0.0000000 0.0000000 0.00000000 0.2217697 0.05060747 0.41239861 0.2013143
29 0.0000000 0.0000000 0.00000000 0.2654165 0.05722138 0.18844562 0.0000000
30 0.0000000 0.0000000 0.00000000 0.0000000 0.05369700 0.08690413 0.4133656
31 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.3044864
32 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.2732066
33 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.14998883 0.0000000
34 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.5868292
35 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
36 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
37 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
38 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
39 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
40 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
41 0.0000000 0.0000000 0.00000000 0.0000000 0.00000000 0.00000000 0.0000000
7 8 9 10 11 12
7 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
8 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
9 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
10 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
11 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
12 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
13 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
14 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
15 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
16 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
17 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
18 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
19 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
20 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
21 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
22 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
23 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
24 0.04412072 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
25 0.00000000 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
26 0.00000000 0.00000000 0.1450212 0.000000000 0.00000000 0.000000e+00
27 0.00000000 0.01632467 0.0000000 0.000000000 0.00000000 0.000000e+00
28 0.11390994 0.00000000 0.0000000 0.000000000 0.00000000 0.000000e+00
29 0.06452729 0.00000000 0.4139431 0.010446083 0.00000000 0.000000e+00
30 0.06034916 0.01962399 0.3627066 0.003353524 0.00000000 2.026387e-10
31 0.00000000 0.10189439 0.5246796 0.008617451 0.06032216 0.000000e+00
32 0.40023076 0.02605364 0.2398674 0.000000000 0.06064158 2.691547e-10
33 0.10378674 0.10069475 0.6340828 0.011446921 0.00000000 3.456871e-10
34 0.00000000 0.14734101 0.0000000 0.033229564 0.23260024 0.000000e+00
35 0.15825645 0.10399561 0.4614528 0.035691828 0.24060327 0.000000e+00
36 0.00000000 0.00000000 0.0000000 0.066376088 0.48262668 1.995328e-09
37 0.00000000 0.20750251 0.0000000 0.071138344 0.72135903 0.000000e+00
38 0.00000000 0.10167557 0.0000000 0.105797535 0.00000000 0.000000e+00
39 0.00000000 0.00000000 0.6962935 0.074407486 0.22929899 4.534619e-09
40 0.00000000 0.15464452 0.4710289 0.041814034 0.33251249 8.519749e-10
41 0.00000000 0.00000000 0.0000000 0.084877699 0.34765438 5.174171e-09
13 14 15
7 0.000000e+00 0.0000000 0.000000e+00
8 0.000000e+00 0.0000000 0.000000e+00
9 0.000000e+00 0.0000000 0.000000e+00
10 0.000000e+00 0.0000000 0.000000e+00
11 0.000000e+00 0.0000000 0.000000e+00
12 0.000000e+00 0.0000000 0.000000e+00
13 0.000000e+00 0.0000000 0.000000e+00
14 0.000000e+00 0.0000000 0.000000e+00
15 0.000000e+00 0.0000000 0.000000e+00
16 0.000000e+00 0.0000000 0.000000e+00
17 0.000000e+00 0.0000000 0.000000e+00
18 0.000000e+00 0.0000000 0.000000e+00
19 0.000000e+00 0.0000000 0.000000e+00
20 0.000000e+00 0.0000000 0.000000e+00
21 0.000000e+00 0.0000000 0.000000e+00
22 0.000000e+00 0.0000000 0.000000e+00
23 0.000000e+00 0.0000000 0.000000e+00
24 0.000000e+00 0.0000000 0.000000e+00
25 0.000000e+00 0.0000000 0.000000e+00
26 0.000000e+00 0.0000000 0.000000e+00
27 0.000000e+00 0.0000000 0.000000e+00
28 0.000000e+00 0.0000000 0.000000e+00
29 0.000000e+00 0.0000000 0.000000e+00
30 0.000000e+00 0.0000000 0.000000e+00
31 0.000000e+00 0.0000000 0.000000e+00
32 0.000000e+00 0.0000000 0.000000e+00
33 0.000000e+00 0.0000000 0.000000e+00
34 0.000000e+00 0.0000000 0.000000e+00
35 0.000000e+00 0.0000000 0.000000e+00
36 1.098383e-07 0.4509971 0.000000e+00
37 1.183897e-07 0.0000000 0.000000e+00
38 1.176692e-07 0.7925268 0.000000e+00
39 0.000000e+00 0.0000000 0.000000e+00
40 9.379858e-08 0.0000000 0.000000e+00
41 1.898843e-07 0.5674677 4.063329e-97
Method: Hoenig & Heisey
Value
ConvergenceThreshold 1e-04
Iterations 245
Converged TRUE
0 1 2 3 4
7 9.999999e-01 8.509212e-08 9.980984e-10 8.205526e-15 4.059003e-16
8 9.999980e-01 1.977944e-06 1.092574e-08 9.269287e-14 6.574612e-15
9 9.999667e-01 3.320372e-05 1.080429e-07 1.012163e-12 1.032603e-13
10 9.995966e-01 4.024141e-04 9.648831e-07 1.068031e-11 1.572081e-12
11 9.964797e-01 3.512570e-03 7.763152e-06 1.086423e-10 2.314442e-11
12 9.781409e-01 2.180354e-02 5.556115e-05 1.051913e-09 3.253361e-10
13 9.072961e-01 9.236441e-02 3.394685e-04 9.303634e-09 4.190426e-09
14 7.473841e-01 2.509518e-01 1.664008e-03 7.063977e-08 4.647898e-08
15 5.519368e-01 4.414562e-01 6.606057e-03 4.648079e-07 4.481580e-07
16 4.108260e-01 5.652869e-01 2.387991e-02 2.979872e-06 4.223320e-06
17 3.372943e-01 5.766251e-01 8.601738e-02 2.036953e-05 4.256815e-05
18 2.819469e-01 4.325003e-01 2.849885e-01 1.370404e-04 4.235924e-04
19 1.774725e-01 1.764190e-01 6.423240e-01 6.711172e-04 3.077812e-03
20 7.463514e-02 3.472275e-02 8.737964e-01 2.122627e-03 1.448806e-02
21 2.650131e-02 4.167305e-03 9.066889e-01 5.479457e-03 5.583611e-02
22 8.636087e-03 3.314997e-04 7.800322e-01 1.254885e-02 1.915011e-01
23 2.147258e-03 1.453079e-05 4.625564e-01 2.119652e-02 4.859260e-01
24 3.346613e-04 2.883438e-07 1.553286e-01 2.169483e-02 7.494601e-01
25 3.758483e-05 2.977684e-09 3.395505e-02 1.546716e-02 8.076776e-01
26 3.636076e-06 1.913025e-11 5.776318e-03 9.182375e-03 7.270532e-01
27 3.031844e-07 7.650279e-14 7.651237e-04 4.541819e-03 5.469822e-01
28 1.949667e-08 1.704019e-16 7.061102e-05 1.674794e-03 3.077409e-01
29 8.871921e-10 1.939707e-19 4.165789e-06 4.224478e-04 1.188027e-01
30 2.980423e-11 1.177231e-22 1.639100e-07 7.604396e-05 3.283186e-02
31 8.012680e-13 4.129409e-26 4.662662e-09 1.058944e-05 7.040928e-03
32 1.761591e-14 8.554651e-30 9.798736e-11 1.165696e-06 1.197338e-03
33 3.082432e-16 1.018683e-33 1.480635e-12 9.872702e-08 1.571414e-04
34 4.198978e-18 6.820215e-38 1.573504e-14 6.292525e-09 1.556866e-05
35 4.534457e-20 2.614265e-42 1.197567e-16 3.073424e-10 1.185683e-06
36 4.045452e-22 5.978913e-47 6.802557e-19 1.198828e-11 7.233884e-08
37 3.079426e-24 8.425907e-52 2.978420e-21 3.856816e-13 3.651411e-09
38 2.026695e-26 7.414604e-57 1.018582e-23 1.037036e-14 1.545223e-10
39 1.152909e-28 4.072942e-62 2.720038e-26 2.329828e-16 5.480690e-12
40 5.634904e-31 1.388271e-67 5.637918e-29 4.347256e-18 1.619531e-13
41 2.353456e-33 2.920311e-73 9.021343e-32 6.700569e-20 3.965488e-15
5 6 7 8 9
7 5.359797e-18 6.402268e-21 2.020887e-18 6.298810e-21 9.615409e-25
8 6.323221e-17 1.634471e-19 1.779202e-17 4.574960e-20 2.366695e-23
9 7.587242e-16 4.045792e-18 1.655420e-16 3.621125e-19 5.938544e-22
10 9.256580e-15 9.706845e-17 1.627258e-15 3.122429e-18 1.518611e-20
11 1.145486e-13 2.251918e-15 1.685859e-14 2.926080e-17 3.948149e-19
12 1.419668e-12 4.987832e-14 1.817557e-13 2.942451e-16 1.030400e-17
13 1.691089e-11 1.012235e-12 1.956958e-12 3.047103e-15 2.590650e-16
14 1.819540e-10 1.768860e-11 1.977583e-11 3.053881e-14 5.897050e-15
15 1.785154e-09 2.686901e-10 1.893438e-10 2.990254e-13 1.226839e-13
16 1.795482e-08 3.988675e-09 1.931091e-09 3.216083e-12 2.622645e-12
17 2.025990e-07 6.332621e-08 2.295881e-08 4.157851e-11 6.304488e-11
18 2.367386e-06 9.925244e-07 2.937079e-07 5.964279e-10 1.573053e-09
19 2.118723e-05 1.135794e-05 2.990195e-06 7.020894e-09 3.013133e-08
20 1.288536e-04 8.419812e-05 2.149535e-05 6.017495e-08 3.931135e-07
21 6.729742e-04 5.109897e-04 1.378839e-04 4.745596e-07 4.414740e-06
22 3.280911e-03 2.759581e-03 8.578685e-04 3.743102e-06 4.638676e-05
23 1.241298e-02 1.102522e-02 4.303855e-03 2.454879e-05 3.791198e-04
24 2.994196e-02 2.677200e-02 1.430412e-02 1.099823e-04 1.980108e-03
25 5.293445e-02 4.542091e-02 3.620452e-02 3.869380e-04 7.597370e-03
26 8.199326e-02 6.436349e-02 8.342384e-02 1.277949e-03 2.559923e-02
27 1.113370e-01 7.622059e-02 1.750989e-01 3.964414e-03 7.579141e-02
28 1.185903e-01 6.749636e-02 2.995496e-01 1.033628e-02 1.764285e-01
29 9.091387e-02 4.100977e-02 3.832392e-01 2.078230e-02 2.962765e-01
30 5.233384e-02 1.783581e-02 3.825485e-01 3.361752e-02 3.744592e-01
31 2.452128e-02 6.019130e-03 3.229649e-01 4.742614e-02 3.861247e-01
32 9.556503e-03 1.610636e-03 2.356480e-01 5.962622e-02 3.319357e-01
33 3.014981e-03 3.325965e-04 1.446258e-01 6.502168e-02 2.315355e-01
34 7.531819e-04 5.184360e-05 7.303010e-02 6.015625e-02 1.281796e-01
35 1.517103e-04 6.211547e-06 3.089597e-02 4.808117e-02 5.734924e-02
36 2.567784e-05 5.961559e-07 1.141233e-02 3.459947e-02 2.161088e-02
37 3.771648e-06 4.733435e-08 3.801195e-03 2.315074e-02 7.083605e-03
38 4.871785e-07 3.150681e-09 1.156896e-03 1.459542e-02 2.046577e-03
39 5.532244e-08 1.757584e-10 3.216391e-04 8.667548e-03 5.210339e-04
40 5.489938e-09 8.167853e-12 8.119709e-05 4.819487e-03 1.161888e-04
41 4.735108e-10 3.145020e-13 1.851197e-05 2.495592e-03 2.257185e-05
10 11 12 13 14
7 3.482067e-21 2.024162e-23 1.413612e-25 2.501565e-25 2.166190e-26
8 2.209924e-20 1.787360e-22 1.749231e-24 1.321938e-24 1.894079e-25
9 1.549896e-19 1.732162e-21 2.338621e-23 7.906673e-24 1.842985e-24
10 1.200821e-18 1.841792e-20 3.377024e-22 5.350879e-23 1.994957e-23
11 1.025313e-17 2.143480e-19 5.254379e-21 4.087490e-22 2.396539e-22
12 9.526249e-17 2.695940e-18 8.697742e-20 3.479955e-21 3.154713e-21
13 9.242720e-16 3.516722e-17 1.469992e-18 3.168845e-20 4.367016e-20
14 8.800810e-15 4.471320e-16 2.383851e-17 2.900491e-19 5.974367e-19
15 8.302218e-14 5.593796e-15 3.744575e-16 2.693945e-18 8.154264e-18
16 8.723414e-13 7.741465e-14 6.405567e-15 2.854466e-17 1.248348e-16
17 1.117273e-11 1.297014e-12 1.305882e-13 3.776065e-16 2.345871e-15
18 1.610041e-10 2.428265e-11 2.928639e-12 5.756482e-15 4.994762e-14
19 1.930714e-09 3.757294e-10 5.343696e-11 7.479560e-14 8.911805e-13
20 1.709407e-08 4.263102e-09 7.038418e-10 7.349194e-13 1.182226e-11
21 1.412156e-07 4.482397e-08 8.457236e-09 6.900980e-12 1.473607e-10
22 1.183159e-06 4.747262e-07 1.007665e-07 6.731370e-11 1.875961e-09
23 8.358322e-06 4.210330e-06 9.897603e-07 5.670347e-10 2.027767e-08
24 4.090223e-05 2.569010e-05 6.584254e-06 3.388955e-09 1.528980e-07
25 1.593891e-04 1.239720e-04 3.410182e-05 1.651976e-08 9.244984e-07
26 5.912638e-04 5.656105e-04 1.643881e-04 7.851466e-08 5.358693e-06
27 2.089081e-03 2.441109e-03 7.379471e-04 3.640385e-07 2.979202e-05
28 6.290817e-03 8.917833e-03 2.760378e-03 1.473396e-06 1.421530e-04
29 1.481358e-02 2.530215e-02 7.894486e-03 4.776294e-06 5.341342e-04
30 2.845863e-02 5.816761e-02 1.800905e-02 1.293783e-05 1.648856e-03
31 4.835100e-02 1.174538e-01 3.552271e-02 3.174445e-05 4.533045e-03
32 7.423728e-02 2.128644e-01 6.190950e-02 7.209367e-05 1.134121e-02
33 1.002531e-01 3.369945e-01 9.278513e-02 1.474972e-04 2.513190e-02
34 1.164751e-01 4.558549e-01 1.169687e-01 2.659058e-04 4.824892e-02
35 1.185490e-01 5.365183e-01 1.262993e-01 4.301297e-04 8.171778e-02
36 1.101591e-01 5.725654e-01 1.217310e-01 6.506194e-04 1.272449e-01
37 9.651653e-02 5.722017e-01 1.081610e-01 9.504110e-04 1.881310e-01
38 8.079731e-02 5.426398e-01 8.977695e-02 1.358651e-03 2.676279e-01
39 6.460678e-02 4.881855e-01 6.959142e-02 1.900151e-03 3.662059e-01
40 4.905030e-02 4.141572e-01 5.007717e-02 2.584336e-03 4.791141e-01
41 3.516668e-02 3.295310e-01 3.327060e-02 3.399648e-03 5.960953e-01
15
7 6.066447e-93
8 2.558161e-92
9 1.244987e-91
10 6.990547e-91
11 4.517707e-90
12 3.317956e-89
13 2.657628e-88
14 2.181831e-87
15 1.853340e-86
16 1.831338e-85
17 2.303672e-84
18 3.405151e-83
19 4.374351e-82
20 4.333073e-81
21 4.182599e-80
22 4.276403e-79
23 3.850212e-78
24 2.507848e-77
25 1.358500e-76
26 7.316241e-76
27 3.919458e-75
28 1.868960e-74
29 7.278367e-74
30 2.415055e-73
31 7.401443e-73
32 2.140865e-72
33 5.688264e-72
34 1.357963e-71
35 2.966089e-71
36 6.177273e-71
37 1.266854e-70
38 2.592560e-70
39 5.292675e-70
40 1.071427e-69
41 2.139118e-69
Method: Gascuel
Value
ConvergenceThreshold 1e-04
alpha 0.112751
beta 0.07044978
gamma 0.05807639
Converged TRUE
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