Description Usage Arguments Details Value Author(s) References See Also Examples
The NBF()
function defines the Negative Binomial family distribution, a three parameter distribution, for a gamlss.family
object to be used in GAMLSS fitting using the function gamlss()
.
The functions dNBF
, pNBF
, qNBF
and rNBF
define the density, distribution function, quantile function and random generation for the negative binomial family, NBF()
, distribution.
The functions dZINBF
, pZINBF
, qZINBF
and rZINBF
define the density, distribution function, quantile function and random generation for the zero inflated negative binomial family, ZINBF()
, distribution a four parameter distribution.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | NBF(mu.link = "log", sigma.link = "log", nu.link = "log")
dNBF(x, mu = 1, sigma = 1, nu = 2, log = FALSE)
pNBF(q, mu = 1, sigma = 1, nu = 2, lower.tail = TRUE, log.p = FALSE)
qNBF(p, mu = 1, sigma = 1, nu = 2, lower.tail = TRUE, log.p = FALSE)
rNBF(n, mu = 1, sigma = 1, nu = 2)
ZINBF(mu.link = "log", sigma.link = "log", nu.link = "log",
tau.link = "logit")
dZINBF(x, mu = 1, sigma = 1, nu = 2, tau = 0.1, log = FALSE)
pZINBF(q, mu = 1, sigma = 1, nu = 2, tau = 0.1, lower.tail = TRUE,
log.p = FALSE)
qZINBF(p, mu = 1, sigma = 1, nu = 2, tau = 0.1, lower.tail = TRUE,
log.p = FALSE)
rZINBF(n, mu = 1, sigma = 1, nu = 2, tau = 0.1)
|
mu.link |
The link function for |
sigma.link |
The link function for |
nu.link |
The link function for |
tau.link |
The link function for |
x |
vector of (non-negative integer) |
mu |
vector of positive means |
sigma |
vector of positive dispersion parameter |
nu |
vector of power parameter |
tau |
vector of inflation parameter |
log, log.p |
logical; if TRUE, probabilities p are given as log(p) |
lower.tail |
logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x] |
p |
vector of probabilities |
q |
vector of quantiles |
n |
number of random values to return |
The definition for Negative Binomial Family distribution , NBF
, is similar to the Negative Binomial type I. The probability function of the NBF
can be obtained by replacing σ with σ μ^{ν-2} where ν is a power parameter.
The distribution has mean μ and variance μ+σ μ^{ν}.
returns a gamlss.family
object which can be used to fit a Negative Binomial Family distribution in the gamlss()
function.
Bob Rigby and Mikis Stasinopoulos
Anscombe, F. J. (1950) Sampling theory of the negative binomial and logarithmic distributions, Biometrika, 37, 358-382.
Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion), Appl. Statist., 54, part 3, pp 507-554.
Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC. An older version can be found in http://www.gamlss.com/.
Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.com/).
Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.
Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017) Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.
Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017) Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | NBF() # default link functions for the Negative Binomial Family
# plotting the distribution
plot(function(y) dNBF(y, mu = 10, sigma = 0.5, nu=2 ), from=0,
to=40, n=40+1, type="h")
# creating random variables and plot them
tN <- table(Ni <- rNBF(1000, mu=5, sigma=0.5, nu=2))
r <- barplot(tN, col='lightblue')
# zero inflated NBF
ZINBF() # default link functions for the zero inflated NBF
# plotting the distribution
plot(function(y) dZINBF(y, mu = 10, sigma = 0.5, nu=2, tau=.1 ),
from=0, to=40, n=40+1, type="h")
# creating random variables and plot them
tN <- table(Ni <- rZINBF(1000, mu=5, sigma=0.5, nu=2, tau=0.1))
r <- barplot(tN, col='lightblue')
## Not run:
library(gamlss)
data(species)
species <- transform(species, x=log(lake))
m6 <- gamlss(fish~poly(x,2), sigma.fo=~1, data=species, family=NBF,
n.cyc=200)
fitted(m6, "nu")[1]
## End(Not run)
|
Loading required package: MASS
GAMLSS Family: NBF NB Family
Link function for mu : log
Link function for sigma: log
Link function for nu : log
GAMLSS Family: ZINBF
Link function for mu : log
Link function for sigma: log
Link function for nu : log
Link function for tau : logit
Loading required package: splines
Loading required package: gamlss.data
Attaching package: 'gamlss.data'
The following object is masked from 'package:datasets':
sleep
Loading required package: nlme
Loading required package: parallel
********** GAMLSS Version 5.1-3 **********
For more on GAMLSS look at http://www.gamlss.org/
Type gamlssNews() to see new features/changes/bug fixes.
GAMLSS-RS iteration 1: Global Deviance = 614.1349
GAMLSS-RS iteration 2: Global Deviance = 613.7821
GAMLSS-RS iteration 3: Global Deviance = 613.4428
GAMLSS-RS iteration 4: Global Deviance = 613.1159
GAMLSS-RS iteration 5: Global Deviance = 612.8035
GAMLSS-RS iteration 6: Global Deviance = 612.5025
GAMLSS-RS iteration 7: Global Deviance = 612.2054
GAMLSS-RS iteration 8: Global Deviance = 611.9217
GAMLSS-RS iteration 9: Global Deviance = 611.6472
GAMLSS-RS iteration 10: Global Deviance = 611.3866
GAMLSS-RS iteration 11: Global Deviance = 611.1413
GAMLSS-RS iteration 12: Global Deviance = 610.9056
GAMLSS-RS iteration 13: Global Deviance = 610.6826
GAMLSS-RS iteration 14: Global Deviance = 610.4682
GAMLSS-RS iteration 15: Global Deviance = 610.2649
GAMLSS-RS iteration 16: Global Deviance = 610.0689
GAMLSS-RS iteration 17: Global Deviance = 609.8839
GAMLSS-RS iteration 18: Global Deviance = 609.705
GAMLSS-RS iteration 19: Global Deviance = 609.5371
GAMLSS-RS iteration 20: Global Deviance = 609.3739
GAMLSS-RS iteration 21: Global Deviance = 609.2215
GAMLSS-RS iteration 22: Global Deviance = 609.0729
GAMLSS-RS iteration 23: Global Deviance = 608.9346
GAMLSS-RS iteration 24: Global Deviance = 608.7995
GAMLSS-RS iteration 25: Global Deviance = 608.6739
GAMLSS-RS iteration 26: Global Deviance = 608.5513
GAMLSS-RS iteration 27: Global Deviance = 608.4374
GAMLSS-RS iteration 28: Global Deviance = 608.3263
GAMLSS-RS iteration 29: Global Deviance = 608.2228
GAMLSS-RS iteration 30: Global Deviance = 608.1224
GAMLSS-RS iteration 31: Global Deviance = 608.0284
GAMLSS-RS iteration 32: Global Deviance = 607.9376
GAMLSS-RS iteration 33: Global Deviance = 607.8522
GAMLSS-RS iteration 34: Global Deviance = 607.7701
GAMLSS-RS iteration 35: Global Deviance = 607.6927
GAMLSS-RS iteration 36: Global Deviance = 607.6184
GAMLSS-RS iteration 37: Global Deviance = 607.5481
GAMLSS-RS iteration 38: Global Deviance = 607.4808
GAMLSS-RS iteration 39: Global Deviance = 607.417
GAMLSS-RS iteration 40: Global Deviance = 607.356
GAMLSS-RS iteration 41: Global Deviance = 607.2981
GAMLSS-RS iteration 42: Global Deviance = 607.2428
GAMLSS-RS iteration 43: Global Deviance = 607.1903
GAMLSS-RS iteration 44: Global Deviance = 607.1401
GAMLSS-RS iteration 45: Global Deviance = 607.0924
GAMLSS-RS iteration 46: Global Deviance = 607.0468
GAMLSS-RS iteration 47: Global Deviance = 607.0034
GAMLSS-RS iteration 48: Global Deviance = 606.9621
GAMLSS-RS iteration 49: Global Deviance = 606.9226
GAMLSS-RS iteration 50: Global Deviance = 606.885
GAMLSS-RS iteration 51: Global Deviance = 606.8491
GAMLSS-RS iteration 52: Global Deviance = 606.8149
GAMLSS-RS iteration 53: Global Deviance = 606.7823
GAMLSS-RS iteration 54: Global Deviance = 606.7511
GAMLSS-RS iteration 55: Global Deviance = 606.7214
GAMLSS-RS iteration 56: Global Deviance = 606.693
GAMLSS-RS iteration 57: Global Deviance = 606.6659
GAMLSS-RS iteration 58: Global Deviance = 606.64
GAMLSS-RS iteration 59: Global Deviance = 606.6153
GAMLSS-RS iteration 60: Global Deviance = 606.5917
GAMLSS-RS iteration 61: Global Deviance = 606.5622
GAMLSS-RS iteration 62: Global Deviance = 606.5334
GAMLSS-RS iteration 63: Global Deviance = 606.506
GAMLSS-RS iteration 64: Global Deviance = 606.4802
GAMLSS-RS iteration 65: Global Deviance = 606.4559
GAMLSS-RS iteration 66: Global Deviance = 606.4329
GAMLSS-RS iteration 67: Global Deviance = 606.4112
GAMLSS-RS iteration 68: Global Deviance = 606.3907
GAMLSS-RS iteration 69: Global Deviance = 606.3714
GAMLSS-RS iteration 70: Global Deviance = 606.3532
GAMLSS-RS iteration 71: Global Deviance = 606.336
GAMLSS-RS iteration 72: Global Deviance = 606.3198
GAMLSS-RS iteration 73: Global Deviance = 606.3045
GAMLSS-RS iteration 74: Global Deviance = 606.29
GAMLSS-RS iteration 75: Global Deviance = 606.2764
GAMLSS-RS iteration 76: Global Deviance = 606.2636
GAMLSS-RS iteration 77: Global Deviance = 606.2515
GAMLSS-RS iteration 78: Global Deviance = 606.2405
GAMLSS-RS iteration 79: Global Deviance = 606.2369
GAMLSS-RS iteration 80: Global Deviance = 606.2332
GAMLSS-RS iteration 81: Global Deviance = 606.2296
GAMLSS-RS iteration 82: Global Deviance = 606.226
GAMLSS-RS iteration 83: Global Deviance = 606.2225
GAMLSS-RS iteration 84: Global Deviance = 606.2191
GAMLSS-RS iteration 85: Global Deviance = 606.2158
GAMLSS-RS iteration 86: Global Deviance = 606.2125
GAMLSS-RS iteration 87: Global Deviance = 606.2093
GAMLSS-RS iteration 88: Global Deviance = 606.2062
GAMLSS-RS iteration 89: Global Deviance = 606.2031
GAMLSS-RS iteration 90: Global Deviance = 606.2001
GAMLSS-RS iteration 91: Global Deviance = 606.1972
GAMLSS-RS iteration 92: Global Deviance = 606.1943
GAMLSS-RS iteration 93: Global Deviance = 606.1915
GAMLSS-RS iteration 94: Global Deviance = 606.1888
GAMLSS-RS iteration 95: Global Deviance = 606.1861
GAMLSS-RS iteration 96: Global Deviance = 606.1799
GAMLSS-RS iteration 97: Global Deviance = 606.1753
GAMLSS-RS iteration 98: Global Deviance = 606.1707
GAMLSS-RS iteration 99: Global Deviance = 606.1664
GAMLSS-RS iteration 100: Global Deviance = 606.1623
GAMLSS-RS iteration 101: Global Deviance = 606.1582
GAMLSS-RS iteration 102: Global Deviance = 606.1544
GAMLSS-RS iteration 103: Global Deviance = 606.1507
GAMLSS-RS iteration 104: Global Deviance = 606.1471
GAMLSS-RS iteration 105: Global Deviance = 606.1437
GAMLSS-RS iteration 106: Global Deviance = 606.1404
GAMLSS-RS iteration 107: Global Deviance = 606.1372
GAMLSS-RS iteration 108: Global Deviance = 606.1342
GAMLSS-RS iteration 109: Global Deviance = 606.1312
GAMLSS-RS iteration 110: Global Deviance = 606.1284
GAMLSS-RS iteration 111: Global Deviance = 606.1257
GAMLSS-RS iteration 112: Global Deviance = 606.1231
GAMLSS-RS iteration 113: Global Deviance = 606.1205
GAMLSS-RS iteration 114: Global Deviance = 606.1181
GAMLSS-RS iteration 115: Global Deviance = 606.1157
GAMLSS-RS iteration 116: Global Deviance = 606.1135
GAMLSS-RS iteration 117: Global Deviance = 606.1113
GAMLSS-RS iteration 118: Global Deviance = 606.1092
GAMLSS-RS iteration 119: Global Deviance = 606.1072
GAMLSS-RS iteration 120: Global Deviance = 606.1052
GAMLSS-RS iteration 121: Global Deviance = 606.1033
GAMLSS-RS iteration 122: Global Deviance = 606.1015
GAMLSS-RS iteration 123: Global Deviance = 606.0998
GAMLSS-RS iteration 124: Global Deviance = 606.0981
GAMLSS-RS iteration 125: Global Deviance = 606.0964
GAMLSS-RS iteration 126: Global Deviance = 606.0949
GAMLSS-RS iteration 127: Global Deviance = 606.0933
GAMLSS-RS iteration 128: Global Deviance = 606.0919
GAMLSS-RS iteration 129: Global Deviance = 606.0905
GAMLSS-RS iteration 130: Global Deviance = 606.0891
GAMLSS-RS iteration 131: Global Deviance = 606.088
GAMLSS-RS iteration 132: Global Deviance = 606.0862
GAMLSS-RS iteration 133: Global Deviance = 606.0837
GAMLSS-RS iteration 134: Global Deviance = 606.0827
[1] 2.84052
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