KINBF: K-inflated Negative Binomial Family distributions for fitting...
In gamlss.countKinf: Generating and Fitting K-Inflated 'discrete gamlss.family' Distributions

Description Usage Arguments Details Value Author(s) References See Also Examples

The function KINBF defines the K-inflated Negative Binomial Family distribution, a four parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss(). The functions dKINBF, pKINBF, qKINBF and rKINBF define the density, distribution function, quantile function and random generation for the K-inflated Negative Binomial Family, KINBF(), distribution.

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

dKINBF(x, mu = 1, sigma = 1, nu = 2, tau = 0.1, kinf=0, log = FALSE)

pKINBF(q, mu = 1, sigma = 1, nu = 2, tau = 0.1, kinf=0, lower.tail = TRUE,
            log.p = FALSE)

qKINBF(p, mu = 1, sigma = 1, nu = 2, tau = 0.1, kinf=0, lower.tail = TRUE,
            log.p = FALSE)

rKINBF(n, mu = 1, sigma = 1, nu = 2, kinf=0, tau = 0.1)

`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 "log" link as the default for the nu parameter
`tau.link`	Defines the `tau.link`, with "logit" link as the default for the tau parameter
`x`	vector of (non-negative integer) quantiles
`mu`	vector of positive means
`sigma`	vector of positive despersion parameter
`nu`	vector of nu
`tau`	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]

The definition for the K-inflated Negative Binomial Family distribution.

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

Saeed Mohammadpour <s.mohammadpour1111@gamlil.com>, Mikis Stasinopoulos <d.stasinopoulos@londonmet.ac.uk>

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.

gamlss.family, KINBF

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

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

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

# generate random sample from zero inflated Negative Binomial Family distribution
x<-rinf0NBF(1000,mu=1, sigma=.5, nu=-.2, tau=.2)

# fit the zero inflated Negative Binomial Family distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf0NBF, data=data)
histDist(x, family=inf0NBF)
## End(Not run)
#--------------------------------------------------------------------------------

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

# generate random sample from one inflated Negative Binomial Family distribution
x<-rinf1NBF(1000,mu=1, sigma=.5, nu=-.2, tau=.2)

# fit the one inflated Negative Binomial Family distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf1NBF, data=data)
histDist(x, family=inf1NBF)
## End(Not run)
#--------------------------------------------------------------------------------

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

#plot the pdf using plot
plot(function(x) dinf1NBF(x, mu=mu, sigma=sigma, nu=nu, tau=tau), 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,pinf1NBF(0:19, mu=mu, sigma=sigma, nu=nu, tau=tau)), 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), qinf1NBF(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 <- rinf1NBF(1000, mu=mu, sigma=sigma, nu=nu, tau=tau)
 hist(Ni,breaks=seq(min(Ni)-0.5,max(Ni)+0.5,by=1),col="lightgray", main="",cex.lab=2)
barplot(table(Ni))
#--------------------------------------------------------------------------------