KIDPO: K-inflated Double Poisson distributions for fitting a GAMLSS...
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 KIDPO defines the K-inflated Double Poisson distribution, a three parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss(). The functions dKIDPO, pKIDPO, qKIDPO and rKIDPO define the density, distribution function, quantile function and random generation for the K-inflated Double Poisson, KIDPO(), distribution.

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

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

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

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

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

`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]

The definition for the K-inflated Double Poisson distribution.

The functions KIDPO return a gamlss.family object which can be used to fit K-inflated Double Poisson 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, KIDPO

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

# gives information about the default links for the  Double Poisson distribution
KIDPO()
#--------------------------------------------------------------------------------

# generate zero inflated Double Poisson distribution
gen.Kinf(family=DPO, kinf=0)

# generate random sample from zero inflated Double Poisson distribution
x<-rinf0DPO(1000,mu=1, sigma=.5, nu=.2)

# fit the zero inflated Double Poisson distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf0DPO, data=data)
histDist(x, family=inf0DPO)
## End(Not run)
#--------------------------------------------------------------------------------

# generated one inflated Double Poisson distribution
gen.Kinf(family=DPO, kinf=1)

# generate random sample from one inflated Double Poisson distribution
x<-rinf1DPO(1000,mu=1, sigma=.5, nu=.2)

# fit the one inflated Double Poisson distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf1DPO, data=data)
histDist(x, family=inf1DPO)
## 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) dinf1DPO(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,pinf1DPO(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), qinf1DPO(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 <- rinf1DPO(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))
#--------------------------------------------------------------------------------