NBF: Negative Binomial Family distribution for fitting a GAMLSS

In Stan125/gamlss.dist: Distributions for Generalized Additive Models for Location Scale and Shape

Description

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.

Usage

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)      

Arguments

mu.link	The link function for mu
sigma.link	The link function for sigma
nu.link	The link function for nu
tau.link	The link function for tau
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

Details

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}.

Value

returns a gamlss.family object which can be used to fit a Negative Binomial Family distribution in the gamlss() function.

Author(s)

Bob Rigby and Mikis Stasinopoulos

References

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.

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.org/).

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.

See Also

NBI, NBII

Examples

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)

Stan125/gamlss.dist documentation built on May 12, 2019, 7:38 a.m.