KIBNB: K-inflated Beta Negative Binomial distributions for fitting a...
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 KIBNB defines the K-inflated Beta Negative Binomial distribution, a four parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss().The functions dKIBNB, pKIBNB, qKIBNB and rKIBNB define the density, distribution function, quantile function and random generation for the K-inflated Beta Negative Binomia, KIBNB(), distribution.

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

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

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

qKIBNB(p, mu = 1, sigma = 1, nu = 1, tau = 0.1, kinf=0, lower.tail = TRUE,
            log.p = FALSE, max.value = 10000)

rKIBNB(n, mu = 1, sigma = 1, nu = 1, tau = 0.1, kinf=0, max.value = 10000)

`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]
`max.value`	a constant, set to the default value of 10000 for how far the algorithm should look for q

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

The functions KIBNB return a gamlss.family object which can be used to fit K-inflated Beta Negative Binomial 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, KIBNB

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

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

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

# generate random sample from zero inflated Beta Negative Binomial distribution
x<-rinf0BNB(1000,mu=1, sigma=.5, nu=.2, tau=.2)

# fit the zero inflated Beta Negative Binomial distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf0BNB, data=data)
histDist(x, family=inf0BNB)
## End(Not run)
#-------------------------------------------------------------------------------

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

# generate random sample from one inflated Beta Negative Binomial distribution
x<-rinf1BNB(1000,mu=1, sigma=.5, nu=.2, tau=.2)

# fit the one inflated Beta Negative Binomial distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf1BNB, data=data)
histDist(x, family=inf1BNB)
## 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) dinf1BNB(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,pinf1BNB(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), qinf1BNB(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 <- rinf1BNB(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))
#-------------------------------------------------------------------------------