KINBI: K-inflated Negative Binomial distributions for fitting a...

In gamlss.countKinf: Generating and Fitting K-Inflated 'discrete gamlss.family' Distributions

Description

The function KINBI defines the K-inflated Negative Binomial distribution, a three parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss(). The functions dKINBI, pKINBI, qKINBI and rKINBI define thedensity, distribution function, quantile function and random generation for the K-inflated Negative Binomial,KINBI(), distribution.

Usage

 KINBI(mu.link = "log", sigma.link = "log", nu.link = "logit", kinf="K")

dKINBI(x, mu = 1, sigma = 1, nu = 0.3, kinf=0 ,log = FALSE)

pKINBI(q, mu = 1, sigma = 1, nu = 0.3, kinf=0, lower.tail = TRUE,
    log.p = FALSE)

qKINBI(p, mu = 1, sigma = 1, nu = 0.3, kinf=0, lower.tail = TRUE,
    log.p = FALSE)

rKINBI(n, mu = 1, sigma = 1, nu = 0.3, kinf=0)

Arguments

mu.link	Defines the mu.link, with "log" link as the default for the mu parameter
sigma.link	Defines the sigma.link, with "log" link as the default for the sigma parameter
nu.link	Defines the nu.link, with "logit" link as the default for the nu parameter
x	vector of (non-negative integer) quantiles
mu	vector of positive means
sigma	vector of positive despersion parameter
nu	vector of inflated point probability
p	vector of probabilities
q	vector of quantiles
n	number of random values to return
kinf	defines inflated point in generating K-inflated distribution
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]

Details

The definition for the K-inflated Negative Binomial distribution.

Value

The functions KINBI return a gamlss.family object which can be used to fit K-inflated Negative Binomial distribution in the gamlss() function.

Author(s)

Saeed Mohammadpour <[e-mail]>, Mikis Stasinopoulos <[e-mail]>

References

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.

Rigby, R. A. and Stasinopoulos D. M. (2010) The gamlss.family distributions, (distributed with this package or seehttp://www.gamlss.org/)

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.

Najafabadi, A. T. P. and MohammadPour, S. (2017). A k-Inflated Negative Binomial Mixture Regression Model: Application to Rate-Making Systems. Asia-Pacific Journal of Risk and Insurance, 12.

See Also

gamlss.family, KINBI

Examples

#--------------------------------------------------------------------------------

# gives information about the default links for the  Negative Binomial distribution
KINBI()
#--------------------------------------------------------------------------------

# generate zero inflated Negative Binomial distribution
gen.Kinf(family=NBI, kinf=0)

# generate random sample from zero inflated Negative Binomial distribution
x<-rinf0NBI(1000,mu=1, sigma=.5, nu=.2)

# fit the zero inflated Negative Binomial distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf0NBI, data=data)
histDist(x, family=inf0NBI)
## End(Not run)
#--------------------------------------------------------------------------------

# generated one inflated Negative Binomial distribution
gen.Kinf(family=NBI, kinf=1)

# generate random sample from one inflated Negative Binomial distribution
x<-rinf1NBI(1000,mu=1, sigma=.5, nu=.2)

# fit the one inflated Negative Binomial distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf1NBI, data=data)
histDist(x, family=inf1NBI)
## End(Not run)
#--------------------------------------------------------------------------------

mu=4; sigma=.5; nu=.2;
par(mgp=c(2,1,0),mar=c(4,4,4,1)+0.1)

#plot the pdf using plot
plot(function(x) dinf1NBI(x, mu=mu, sigma=sigma, nu=nu), from=0, to=20, n=20+1,
     type="h",xlab="x",ylab="f(x)",cex.lab=1.5)
#--------------------------------------------------------------------------------

#plot the cdf using plot
cdf <- stepfun(0:19, c(0,pinf1NBI(0:19, mu=mu, sigma=sigma, nu=nu)), f = 0)
plot(cdf, xlab="x", ylab="F(x)", verticals=FALSE,
     cex.points=.8, pch=16, main="",cex.lab=1.5)
#--------------------------------------------------------------------------------

#plot the qdf using plot
invcdf <- stepfun(seq(0.01,.99,length=19), qinf1NBI(seq(0.1,.99,length=20),mu,        sigma), f = 0)
plot(invcdf, ylab=expression(x[p]==F^{-1}(p)), do.points=FALSE,verticals=TRUE,
     cex.points=.8, pch=16, main="",cex.lab=1.5, xlab="p")
#--------------------------------------------------------------------------------

# generate random sample
Ni <- rinf1NBI(1000, mu=mu, sigma=sigma, nu=nu)
 hist(Ni,breaks=seq(min(Ni)-0.5,max(Ni)+0.5,by=1),col="lightgray", main="",cex.lab=2)
barplot(table(Ni))
#--------------------------------------------------------------------------------

gamlss.countKinf documentation built on May 2, 2019, 2:10 p.m.