eptren: Maximum Likelihood Estimates of Intensity Rates
In SAPP: Statistical Analysis of Point Processes
Description
Usage
Arguments
Details
Value
References
Examples
Description
Compute the maximum likelihood estimates of intensity rates of either
exponential polynomial or exponential Fourier series of non-stationary Poisson
process models.
Usage
1
2
Arguments
data
point process data.
mag
magnitude.
threshold
threshold magnitude.
nparam
maximum number of parameters.
nsub
number of subdivisions in either (0,t) or (0,
cycle), where t is the length of observed time interval of
points.
cycle
periodicity to be investigated days in a Poisson process model.
If zero (default) fit an exponential polynomial model.
tmpfile
a character string naming the file to write the process of minimizing by
Davidon-Fletcher-Powell procedure. If "" print the process to the standard
output and if NULL (default) no report.
nlmax
the maximum number of steps in the process of minimizing.
plot
logical. If TRUE (default) intensity rates are plotted.
Details
This function computes the maximum likelihood estimates (MLEs) of the
coefficients A_1, A_2,..., A_n is an exponential
polynomial
f(t) = exp(A_1 + A_2t + A_3t^2 + ... )
or A_1, A_2, B_2, ..., A_n, B_n in a Poisson process model with an
intensity taking the form of an exponential Fourier series
f(t) = exp{ A_1 + A_2cos(2π t/p) + B_2sin(2π t/p) + A_3cos(4π t/p) + B_3sin(4π t/p) +... }
which represents the time varying rate of occurrence (intensity function) of
earthquakes in a region.
These two models belong to the family of non-stationary Poisson process. The
optimal order n can be determined by minimize the value of the Akaike
Information Criterion (AIC).
Value
aic
AIC.
param
parameters.
aicmin
minimum AIC.
maice.order
number of parameters of minimum AIC.
time
time ( cycle = 0 ) or superposed occurrence time
( cycle > 0 ).
intensity
intensity rates.
References
Ogata, Y., Katsura, K. and Zhuang, J. (2006)
Computer Science Monographs, No.32, TIMSAC84: STATISTICAL ANALYSIS OF
SERIES OF EVENTS (TIMSAC84-SASE) VERSION 2.
The Institute of Statistical Mathematics.
Ogata, Y. (2006)
Computer Science Monographs, No.33, Statistical Analysis of Seismicity -
updated version (SASeies2006).
The Institute of Statistical Mathematics.
Examples
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
## The Occurrence Times Data of 627 Blastings
data(Brastings)
# exponential polynomial trend fitting
eptren(Brastings, nparam = 10, nsub = 1000)
# exponential Fourier series fitting
eptren(Brastings, nparam = 10, nsub = 1000, cycle = 1)
## Poisson Process data
data(PoissonData)
# exponential polynomial trend fitting
eptren(PoissonData, nparam = 10, nsub = 1000)
# exponential Fourier series fitting
eptren(PoissonData, nparam = 10, nsub = 1000, cycle = 1)
## The aftershock data of 26th July 2003 earthquake of M6.2
data(main2003JUL26)
x <- main2003JUL26
# exponential polynomial trend fitting
eptren(x$time, mag = x$magnitude, nparam = 10, nsub = 1000)
# exponential Fourier series fitting
eptren(x$time, mag = x$magnitude, nparam = 10, nsub = 1000, cycle = 1)
Example output
AIC -6820.946962
parameters
-1.987778e+00
AIC -6839.492351
parameters
-2.319355e+00 1.376921e-04
AIC -6839.237636
parameters
-2.457719e+00 3.024394e-04 -3.450138e-08
AIC -6842.441583
parameters
-2.177895e+00 -3.857168e-04 3.272058e-07 -5.149384e-11
AIC -6840.460315
parameters
-2.196091e+00 -3.075866e-04 2.525058e-07 -2.661788e-11 -2.679979e-15
AIC -6855.076407
parameters
-2.865567e+00 3.738334e-03 -5.699733e-06 3.347044e-09 -8.152297e-13
6.992849e-17
AIC -6872.954251
parameters
-3.929925e+00 1.152535e-02 -2.142796e-05 1.646287e-08 -6.015396e-12
1.045802e-15 -6.975925e-20
AIC -6874.583056
parameters
-3.380743e+00 6.446511e-03 -7.864977e-06 8.727766e-10 3.018237e-12
-1.722788e-15 3.585472e-19 -2.633018e-23
AIC -6882.490445
parameters
-4.453306e+00 1.879626e-02 -4.993590e-05 6.431146e-08 -4.696754e-11
2.037147e-14 -5.157888e-18 6.999883e-22 -3.918800e-26
AIC -6894.660215
parameters
-6.515836e+00 4.394377e-02 -1.497668e-04 2.480718e-07 -2.304148e-10
1.276257e-13 -4.292136e-17 8.575372e-21 -9.347353e-25 4.277032e-29
minimum AIC -6894.660215
parameters
-6.515836e+00 4.394377e-02 -1.497668e-04 2.480718e-07 -2.304148e-10
1.276257e-13 -4.292136e-17 8.575372e-21 -9.347353e-25 4.277032e-29
AIC 3748.673468
parameters
-1.987778e+00
AIC 2935.917487
parameters
-2.993938e+00 -2.228208e+00 -3.394883e-01
AIC 2795.133600
parameters
-4.591351e+00 -4.349900e+00 -2.211597e+00 -5.115197e-01 -1.646180e+00
AIC 2715.898446
parameters
-3.618100e+00 -2.795589e+00 -7.469769e-01 -9.238863e-02 2.420047e-01
-2.231542e-01 1.119179e+00
AIC 2684.245084
parameters
-3.640266e+00 -2.731892e+00 -9.987121e-01 2.817838e-01 -4.537336e-01
6.111146e-01 5.284477e-01 7.046523e-01 -2.001942e-01
AIC 2678.585427
parameters
-3.746211e+00 -2.760547e+00 -1.283700e+00 4.602742e-01 -5.727876e-01
7.172496e-01 8.983974e-01 4.643990e-01 2.993803e-01 -3.063479e-01
2.610341e-01
AIC 2681.089369
parameters
-3.660020e+00 -2.682327e+00 -1.078178e+00 3.539086e-01 -3.772595e-01
5.807152e-01 8.938055e-01 4.744687e-01 9.816165e-02 -1.346558e-01
8.592809e-02 1.518247e-01 -5.900747e-02
AIC 2679.828724
parameters
-3.727481e+00 -2.854868e+00 -1.092954e+00 1.508242e-01 -4.475855e-01
4.660264e-01 7.296640e-01 5.829483e-01 2.612204e-02 1.766784e-01
2.814307e-01 3.526503e-01 3.465631e-01 2.851646e-02 3.023127e-01
AIC 2683.773579
parameters
-3.739963e+00 -2.870617e+00 -1.121229e+00 1.535853e-01 -4.885361e-01
4.838971e-01 6.927180e-01 6.100064e-01 8.817888e-03 1.914558e-01
2.951647e-01 3.375452e-01 3.858982e-01 -1.152068e-02 3.313167e-01
-3.112560e-02 7.849195e-03
AIC 2686.382934
parameters
-3.870645e+00 -3.042992e+00 -1.332043e+00 1.644134e-01 -7.736482e-01
6.411467e-01 4.630444e-01 8.243812e-01 -1.081159e-01 3.829070e-01
3.273770e-01 3.726283e-01 5.464211e-01 -1.902719e-01 5.277316e-01
-3.001721e-01 7.657180e-02 -1.681358e-01 -2.422645e-02
minimum AIC 2678.585427
parameters
-3.746211e+00 -2.760547e+00 -1.283700e+00 4.602742e-01 -5.727876e-01
7.172496e-01 8.983974e-01 4.643990e-01 2.993803e-01 -3.063479e-01
2.610341e-01
AIC -34948.694674
parameters
-6.719430e-01
AIC -34947.288978
parameters
-6.984868e-01 1.057334e-05
AIC -34946.023292
parameters
-7.371036e-01 5.642344e-05 -9.139568e-09
AIC -34944.023680
parameters
-7.381641e-01 5.893394e-05 -1.038873e-08 1.662081e-13
AIC -34942.263000
parameters
-7.682036e-01 1.772408e-04 -1.162210e-07 3.299465e-11 -3.277889e-15
AIC -34940.312156
parameters
-7.530933e-01 8.801552e-05 7.857379e-09 -3.295030e-11 1.153115e-14
-1.183480e-18
AIC -34938.397580
parameters
-7.747926e-01 2.675485e-04 -3.487105e-07 2.512146e-10 -9.479155e-14
1.750437e-17 -1.244916e-21
AIC -34937.166599
parameters
-8.458696e-01 1.044638e-03 -2.427516e-06 2.549222e-09 -1.354722e-12
3.796251e-16 -5.348098e-20 2.982297e-24
AIC -34938.443948
parameters
-1.008756e+00 3.280636e-03 -1.013818e-05 1.377131e-08 -9.731835e-12
3.853791e-15 -8.624252e-19 1.018940e-22 -4.940700e-27
AIC -34936.634772
parameters
-1.051899e+00 4.005242e-03 -1.326126e-05 1.954106e-08 -1.532236e-11
6.971689e-15 -1.898807e-18 3.045398e-22 -2.644183e-26 9.546751e-31
minimum AIC -34948.694674
parameters
-6.719430e-01
AIC 8538.940185
parameters
-6.719429e-01
AIC 8542.937999
parameters
-6.719433e-01 7.087410e-05 1.306741e-03
AIC 8546.632569
parameters
-6.720033e-01 7.429736e-05 1.297407e-03 -1.468064e-02 -4.874285e-03
AIC 8548.118363
parameters
-6.724951e-01 -1.781599e-04 1.064885e-03 -1.466143e-02 -4.890223e-03
-2.144415e-02 -3.886646e-02
AIC 8551.499430
parameters
-6.726158e-01 2.681432e-04 8.632811e-04 -1.450098e-02 -4.832583e-03
-2.145191e-02 -3.886004e-02 1.773956e-02 1.305705e-02
AIC 8553.599192
parameters
-6.729949e-01 5.600329e-04 1.159915e-03 -1.529546e-02 -5.141845e-03
-2.159176e-02 -3.913959e-02 1.776369e-02 1.306389e-02 -5.192381e-03
-3.825034e-02
AIC 8556.872293
parameters
-6.731421e-01 1.813550e-04 8.917706e-04 -1.526638e-02 -4.886691e-03
-2.188613e-02 -3.958847e-02 1.779290e-02 1.287170e-02 -5.183334e-03
-3.824396e-02 1.095387e-02 -2.121617e-02
AIC 8560.549810
parameters
-6.732044e-01 -1.260564e-05 8.367736e-04 -1.545774e-02 -5.135068e-03
-2.191323e-02 -3.941933e-02 1.768909e-02 1.252489e-02 -5.126004e-03
-3.836174e-02 1.095900e-02 -2.121185e-02 1.110390e-02 -1.138614e-02
AIC 8560.375110
parameters
-6.739932e-01 4.348250e-04 9.479805e-04 -1.485469e-02 -4.789173e-03
-2.144968e-02 -3.843227e-02 1.793473e-02 1.197191e-02 -5.045277e-03
-3.710031e-02 1.067451e-02 -2.086400e-02 1.109814e-02 -1.141520e-02
-4.803230e-02 3.113475e-02
AIC 8562.565622
parameters
-6.743398e-01 -4.114549e-04 3.159351e-04 -1.468348e-02 -4.570659e-03
-2.126116e-02 -3.802860e-02 1.778069e-02 1.266165e-02 -4.696554e-03
-3.732511e-02 1.022304e-02 -2.018761e-02 1.081018e-02 -1.133624e-02
-4.804033e-02 3.112800e-02 -3.759249e-02 -2.759948e-03
minimum AIC 8538.940185
parameters
-6.719429e-01
AIC -31082.473755
parameters
4.815524e+00
AIC -31721.801816
parameters
5.622249e+00 -1.021647e-01
AIC -31735.389914
parameters
5.752456e+00 -1.569067e-01 3.338481e-03
AIC -31746.893407
parameters
5.886683e+00 -2.676148e-01 2.024223e-02 -6.557509e-04
AIC -31856.510480
parameters
6.274930e+00 -8.183626e-01 1.716911e-01 -1.439579e-02 3.903766e-04
AIC -31905.374605
parameters
6.530752e+00 -1.398155e+00 4.213518e-01 -5.333309e-02 2.888323e-03
-5.607666e-05
AIC -31924.658721
parameters
6.693869e+00 -1.934425e+00 7.540239e-01 -1.314154e-01 1.126285e-02
-4.711299e-04 7.709399e-06
AIC -31926.004508
parameters
6.759561e+00 -2.224341e+00 9.986040e-01 -2.113321e-01 2.384907e-02
-1.493119e-03 4.889665e-05 -6.516814e-07
AIC -31931.718100
parameters
6.860822e+00 -2.798592e+00 1.631037e+00 -4.849194e-01 8.269357e-02
-8.403248e-03 4.993332e-04 -1.594508e-05 2.108210e-07
AIC -31938.886232
parameters
6.971855e+00 -3.592573e+00 2.737260e+00 -1.095986e+00 2.538601e-01
-3.549544e-02 3.025126e-03 -1.533196e-04 4.240019e-06 -4.921460e-08
minimum AIC -31938.886232
parameters
6.971855e+00 -3.592573e+00 2.737260e+00 -1.095986e+00 2.538601e-01
-3.549544e-02 3.025126e-03 -1.533196e-04 4.240019e-06 -4.921460e-08
AIC -17587.777268
parameters
4.815570e+00
AIC -17607.560231
parameters
4.811750e+00 1.421437e-01 -2.147652e-02
AIC -17611.230549
parameters
4.809553e+00 1.391681e-01 -2.552836e-02 4.842838e-02 6.578027e-02
AIC -17608.656410
parameters
4.809328e+00 1.376618e-01 -2.635339e-02 4.812782e-02 6.366655e-02
3.565598e-03 3.511790e-02
AIC -17605.871086
parameters
4.809067e+00 1.371395e-01 -2.613830e-02 4.663273e-02 6.349841e-02
2.711055e-03 3.326766e-02 1.394328e-02 2.942081e-02
AIC -17602.227518
parameters
4.808953e+00 1.368650e-01 -2.608699e-02 4.639229e-02 6.358158e-02
1.872969e-03 3.315150e-02 1.350501e-02 2.845042e-02 7.287139e-03
1.606164e-02
AIC -17599.832226
parameters
4.808611e+00 1.365087e-01 -2.602693e-02 4.579720e-02 6.382870e-02
1.465420e-03 3.354824e-02 1.181306e-02 2.872050e-02 5.719056e-03
1.435043e-02 2.530204e-02 2.760591e-02
AIC -17605.521787
parameters
4.806557e+00 1.349376e-01 -2.632390e-02 4.497708e-02 6.422307e-02
1.100673e-04 3.405327e-02 1.064849e-02 2.956136e-02 1.481374e-03
1.473401e-02 2.209395e-02 2.307004e-02 5.445846e-02 7.421021e-02
AIC -17610.252942
parameters
4.804728e+00 1.313130e-01 -2.507258e-02 4.365301e-02 6.437303e-02
-6.680954e-04 3.457566e-02 9.491727e-03 3.052205e-02 7.546003e-04
1.580201e-02 1.825956e-02 2.436158e-02 5.055810e-02 7.093846e-02
6.668741e-02 5.664139e-02
AIC -17607.671319
parameters
4.804524e+00 1.299362e-01 -2.544712e-02 4.210557e-02 6.443794e-02
-1.198090e-03 3.456019e-02 9.196009e-03 3.066868e-02 2.230035e-04
1.605830e-02 1.788318e-02 2.475936e-02 4.899468e-02 7.104570e-02
6.552747e-02 5.494682e-02 1.985910e-02 2.915904e-02
minimum AIC -17611.230549
parameters
4.809553e+00 1.391681e-01 -2.552836e-02 4.842838e-02 6.578027e-02
SAPP documentation built on July 2, 2020, 2:59 a.m.
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Description Usage Arguments Details Value References Examples
Description
Compute the maximum likelihood estimates of intensity rates of either exponential polynomial or exponential Fourier series of non-stationary Poisson process models.
Usage
1 2 |
Arguments
data |
point process data. |
mag |
magnitude. |
threshold |
threshold magnitude. |
nparam |
maximum number of parameters. |
nsub |
number of subdivisions in either (0,t) or (0,
|
cycle |
periodicity to be investigated days in a Poisson process model. If zero (default) fit an exponential polynomial model. |
tmpfile |
a character string naming the file to write the process of minimizing by
Davidon-Fletcher-Powell procedure. If "" print the process to the standard
output and if |
nlmax |
the maximum number of steps in the process of minimizing. |
plot |
logical. If |
Details
This function computes the maximum likelihood estimates (MLEs) of the coefficients A_1, A_2,..., A_n is an exponential polynomial
f(t) = exp(A_1 + A_2t + A_3t^2 + ... )
or A_1, A_2, B_2, ..., A_n, B_n in a Poisson process model with an intensity taking the form of an exponential Fourier series
f(t) = exp{ A_1 + A_2cos(2π t/p) + B_2sin(2π t/p) + A_3cos(4π t/p) + B_3sin(4π t/p) +... }
which represents the time varying rate of occurrence (intensity function) of earthquakes in a region.
These two models belong to the family of non-stationary Poisson process. The optimal order n can be determined by minimize the value of the Akaike Information Criterion (AIC).
Value
aic |
AIC. |
param |
parameters. |
aicmin |
minimum AIC. |
maice.order |
number of parameters of minimum AIC. |
time |
time ( |
intensity |
intensity rates. |
References
Ogata, Y., Katsura, K. and Zhuang, J. (2006) Computer Science Monographs, No.32, TIMSAC84: STATISTICAL ANALYSIS OF SERIES OF EVENTS (TIMSAC84-SASE) VERSION 2. The Institute of Statistical Mathematics.
Ogata, Y. (2006) Computer Science Monographs, No.33, Statistical Analysis of Seismicity - updated version (SASeies2006). The Institute of Statistical Mathematics.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | ## The Occurrence Times Data of 627 Blastings
data(Brastings)
# exponential polynomial trend fitting
eptren(Brastings, nparam = 10, nsub = 1000)
# exponential Fourier series fitting
eptren(Brastings, nparam = 10, nsub = 1000, cycle = 1)
## Poisson Process data
data(PoissonData)
# exponential polynomial trend fitting
eptren(PoissonData, nparam = 10, nsub = 1000)
# exponential Fourier series fitting
eptren(PoissonData, nparam = 10, nsub = 1000, cycle = 1)
## The aftershock data of 26th July 2003 earthquake of M6.2
data(main2003JUL26)
x <- main2003JUL26
# exponential polynomial trend fitting
eptren(x$time, mag = x$magnitude, nparam = 10, nsub = 1000)
# exponential Fourier series fitting
eptren(x$time, mag = x$magnitude, nparam = 10, nsub = 1000, cycle = 1)
|
Example output
AIC -6820.946962
parameters
-1.987778e+00
AIC -6839.492351
parameters
-2.319355e+00 1.376921e-04
AIC -6839.237636
parameters
-2.457719e+00 3.024394e-04 -3.450138e-08
AIC -6842.441583
parameters
-2.177895e+00 -3.857168e-04 3.272058e-07 -5.149384e-11
AIC -6840.460315
parameters
-2.196091e+00 -3.075866e-04 2.525058e-07 -2.661788e-11 -2.679979e-15
AIC -6855.076407
parameters
-2.865567e+00 3.738334e-03 -5.699733e-06 3.347044e-09 -8.152297e-13
6.992849e-17
AIC -6872.954251
parameters
-3.929925e+00 1.152535e-02 -2.142796e-05 1.646287e-08 -6.015396e-12
1.045802e-15 -6.975925e-20
AIC -6874.583056
parameters
-3.380743e+00 6.446511e-03 -7.864977e-06 8.727766e-10 3.018237e-12
-1.722788e-15 3.585472e-19 -2.633018e-23
AIC -6882.490445
parameters
-4.453306e+00 1.879626e-02 -4.993590e-05 6.431146e-08 -4.696754e-11
2.037147e-14 -5.157888e-18 6.999883e-22 -3.918800e-26
AIC -6894.660215
parameters
-6.515836e+00 4.394377e-02 -1.497668e-04 2.480718e-07 -2.304148e-10
1.276257e-13 -4.292136e-17 8.575372e-21 -9.347353e-25 4.277032e-29
minimum AIC -6894.660215
parameters
-6.515836e+00 4.394377e-02 -1.497668e-04 2.480718e-07 -2.304148e-10
1.276257e-13 -4.292136e-17 8.575372e-21 -9.347353e-25 4.277032e-29
AIC 3748.673468
parameters
-1.987778e+00
AIC 2935.917487
parameters
-2.993938e+00 -2.228208e+00 -3.394883e-01
AIC 2795.133600
parameters
-4.591351e+00 -4.349900e+00 -2.211597e+00 -5.115197e-01 -1.646180e+00
AIC 2715.898446
parameters
-3.618100e+00 -2.795589e+00 -7.469769e-01 -9.238863e-02 2.420047e-01
-2.231542e-01 1.119179e+00
AIC 2684.245084
parameters
-3.640266e+00 -2.731892e+00 -9.987121e-01 2.817838e-01 -4.537336e-01
6.111146e-01 5.284477e-01 7.046523e-01 -2.001942e-01
AIC 2678.585427
parameters
-3.746211e+00 -2.760547e+00 -1.283700e+00 4.602742e-01 -5.727876e-01
7.172496e-01 8.983974e-01 4.643990e-01 2.993803e-01 -3.063479e-01
2.610341e-01
AIC 2681.089369
parameters
-3.660020e+00 -2.682327e+00 -1.078178e+00 3.539086e-01 -3.772595e-01
5.807152e-01 8.938055e-01 4.744687e-01 9.816165e-02 -1.346558e-01
8.592809e-02 1.518247e-01 -5.900747e-02
AIC 2679.828724
parameters
-3.727481e+00 -2.854868e+00 -1.092954e+00 1.508242e-01 -4.475855e-01
4.660264e-01 7.296640e-01 5.829483e-01 2.612204e-02 1.766784e-01
2.814307e-01 3.526503e-01 3.465631e-01 2.851646e-02 3.023127e-01
AIC 2683.773579
parameters
-3.739963e+00 -2.870617e+00 -1.121229e+00 1.535853e-01 -4.885361e-01
4.838971e-01 6.927180e-01 6.100064e-01 8.817888e-03 1.914558e-01
2.951647e-01 3.375452e-01 3.858982e-01 -1.152068e-02 3.313167e-01
-3.112560e-02 7.849195e-03
AIC 2686.382934
parameters
-3.870645e+00 -3.042992e+00 -1.332043e+00 1.644134e-01 -7.736482e-01
6.411467e-01 4.630444e-01 8.243812e-01 -1.081159e-01 3.829070e-01
3.273770e-01 3.726283e-01 5.464211e-01 -1.902719e-01 5.277316e-01
-3.001721e-01 7.657180e-02 -1.681358e-01 -2.422645e-02
minimum AIC 2678.585427
parameters
-3.746211e+00 -2.760547e+00 -1.283700e+00 4.602742e-01 -5.727876e-01
7.172496e-01 8.983974e-01 4.643990e-01 2.993803e-01 -3.063479e-01
2.610341e-01
AIC -34948.694674
parameters
-6.719430e-01
AIC -34947.288978
parameters
-6.984868e-01 1.057334e-05
AIC -34946.023292
parameters
-7.371036e-01 5.642344e-05 -9.139568e-09
AIC -34944.023680
parameters
-7.381641e-01 5.893394e-05 -1.038873e-08 1.662081e-13
AIC -34942.263000
parameters
-7.682036e-01 1.772408e-04 -1.162210e-07 3.299465e-11 -3.277889e-15
AIC -34940.312156
parameters
-7.530933e-01 8.801552e-05 7.857379e-09 -3.295030e-11 1.153115e-14
-1.183480e-18
AIC -34938.397580
parameters
-7.747926e-01 2.675485e-04 -3.487105e-07 2.512146e-10 -9.479155e-14
1.750437e-17 -1.244916e-21
AIC -34937.166599
parameters
-8.458696e-01 1.044638e-03 -2.427516e-06 2.549222e-09 -1.354722e-12
3.796251e-16 -5.348098e-20 2.982297e-24
AIC -34938.443948
parameters
-1.008756e+00 3.280636e-03 -1.013818e-05 1.377131e-08 -9.731835e-12
3.853791e-15 -8.624252e-19 1.018940e-22 -4.940700e-27
AIC -34936.634772
parameters
-1.051899e+00 4.005242e-03 -1.326126e-05 1.954106e-08 -1.532236e-11
6.971689e-15 -1.898807e-18 3.045398e-22 -2.644183e-26 9.546751e-31
minimum AIC -34948.694674
parameters
-6.719430e-01
AIC 8538.940185
parameters
-6.719429e-01
AIC 8542.937999
parameters
-6.719433e-01 7.087410e-05 1.306741e-03
AIC 8546.632569
parameters
-6.720033e-01 7.429736e-05 1.297407e-03 -1.468064e-02 -4.874285e-03
AIC 8548.118363
parameters
-6.724951e-01 -1.781599e-04 1.064885e-03 -1.466143e-02 -4.890223e-03
-2.144415e-02 -3.886646e-02
AIC 8551.499430
parameters
-6.726158e-01 2.681432e-04 8.632811e-04 -1.450098e-02 -4.832583e-03
-2.145191e-02 -3.886004e-02 1.773956e-02 1.305705e-02
AIC 8553.599192
parameters
-6.729949e-01 5.600329e-04 1.159915e-03 -1.529546e-02 -5.141845e-03
-2.159176e-02 -3.913959e-02 1.776369e-02 1.306389e-02 -5.192381e-03
-3.825034e-02
AIC 8556.872293
parameters
-6.731421e-01 1.813550e-04 8.917706e-04 -1.526638e-02 -4.886691e-03
-2.188613e-02 -3.958847e-02 1.779290e-02 1.287170e-02 -5.183334e-03
-3.824396e-02 1.095387e-02 -2.121617e-02
AIC 8560.549810
parameters
-6.732044e-01 -1.260564e-05 8.367736e-04 -1.545774e-02 -5.135068e-03
-2.191323e-02 -3.941933e-02 1.768909e-02 1.252489e-02 -5.126004e-03
-3.836174e-02 1.095900e-02 -2.121185e-02 1.110390e-02 -1.138614e-02
AIC 8560.375110
parameters
-6.739932e-01 4.348250e-04 9.479805e-04 -1.485469e-02 -4.789173e-03
-2.144968e-02 -3.843227e-02 1.793473e-02 1.197191e-02 -5.045277e-03
-3.710031e-02 1.067451e-02 -2.086400e-02 1.109814e-02 -1.141520e-02
-4.803230e-02 3.113475e-02
AIC 8562.565622
parameters
-6.743398e-01 -4.114549e-04 3.159351e-04 -1.468348e-02 -4.570659e-03
-2.126116e-02 -3.802860e-02 1.778069e-02 1.266165e-02 -4.696554e-03
-3.732511e-02 1.022304e-02 -2.018761e-02 1.081018e-02 -1.133624e-02
-4.804033e-02 3.112800e-02 -3.759249e-02 -2.759948e-03
minimum AIC 8538.940185
parameters
-6.719429e-01
AIC -31082.473755
parameters
4.815524e+00
AIC -31721.801816
parameters
5.622249e+00 -1.021647e-01
AIC -31735.389914
parameters
5.752456e+00 -1.569067e-01 3.338481e-03
AIC -31746.893407
parameters
5.886683e+00 -2.676148e-01 2.024223e-02 -6.557509e-04
AIC -31856.510480
parameters
6.274930e+00 -8.183626e-01 1.716911e-01 -1.439579e-02 3.903766e-04
AIC -31905.374605
parameters
6.530752e+00 -1.398155e+00 4.213518e-01 -5.333309e-02 2.888323e-03
-5.607666e-05
AIC -31924.658721
parameters
6.693869e+00 -1.934425e+00 7.540239e-01 -1.314154e-01 1.126285e-02
-4.711299e-04 7.709399e-06
AIC -31926.004508
parameters
6.759561e+00 -2.224341e+00 9.986040e-01 -2.113321e-01 2.384907e-02
-1.493119e-03 4.889665e-05 -6.516814e-07
AIC -31931.718100
parameters
6.860822e+00 -2.798592e+00 1.631037e+00 -4.849194e-01 8.269357e-02
-8.403248e-03 4.993332e-04 -1.594508e-05 2.108210e-07
AIC -31938.886232
parameters
6.971855e+00 -3.592573e+00 2.737260e+00 -1.095986e+00 2.538601e-01
-3.549544e-02 3.025126e-03 -1.533196e-04 4.240019e-06 -4.921460e-08
minimum AIC -31938.886232
parameters
6.971855e+00 -3.592573e+00 2.737260e+00 -1.095986e+00 2.538601e-01
-3.549544e-02 3.025126e-03 -1.533196e-04 4.240019e-06 -4.921460e-08
AIC -17587.777268
parameters
4.815570e+00
AIC -17607.560231
parameters
4.811750e+00 1.421437e-01 -2.147652e-02
AIC -17611.230549
parameters
4.809553e+00 1.391681e-01 -2.552836e-02 4.842838e-02 6.578027e-02
AIC -17608.656410
parameters
4.809328e+00 1.376618e-01 -2.635339e-02 4.812782e-02 6.366655e-02
3.565598e-03 3.511790e-02
AIC -17605.871086
parameters
4.809067e+00 1.371395e-01 -2.613830e-02 4.663273e-02 6.349841e-02
2.711055e-03 3.326766e-02 1.394328e-02 2.942081e-02
AIC -17602.227518
parameters
4.808953e+00 1.368650e-01 -2.608699e-02 4.639229e-02 6.358158e-02
1.872969e-03 3.315150e-02 1.350501e-02 2.845042e-02 7.287139e-03
1.606164e-02
AIC -17599.832226
parameters
4.808611e+00 1.365087e-01 -2.602693e-02 4.579720e-02 6.382870e-02
1.465420e-03 3.354824e-02 1.181306e-02 2.872050e-02 5.719056e-03
1.435043e-02 2.530204e-02 2.760591e-02
AIC -17605.521787
parameters
4.806557e+00 1.349376e-01 -2.632390e-02 4.497708e-02 6.422307e-02
1.100673e-04 3.405327e-02 1.064849e-02 2.956136e-02 1.481374e-03
1.473401e-02 2.209395e-02 2.307004e-02 5.445846e-02 7.421021e-02
AIC -17610.252942
parameters
4.804728e+00 1.313130e-01 -2.507258e-02 4.365301e-02 6.437303e-02
-6.680954e-04 3.457566e-02 9.491727e-03 3.052205e-02 7.546003e-04
1.580201e-02 1.825956e-02 2.436158e-02 5.055810e-02 7.093846e-02
6.668741e-02 5.664139e-02
AIC -17607.671319
parameters
4.804524e+00 1.299362e-01 -2.544712e-02 4.210557e-02 6.443794e-02
-1.198090e-03 3.456019e-02 9.196009e-03 3.066868e-02 2.230035e-04
1.605830e-02 1.788318e-02 2.475936e-02 4.899468e-02 7.104570e-02
6.552747e-02 5.494682e-02 1.985910e-02 2.915904e-02
minimum AIC -17611.230549
parameters
4.809553e+00 1.391681e-01 -2.552836e-02 4.842838e-02 6.578027e-02
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