KIYULE: K-inflated Yule distributions for fitting a GAMLSS model
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 KIYULE defines the K-inflated Yule distribution, a two parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss(). The functions dKIYULE, pKIYULE, qKIYULE and rKIYULE define the density, distribution function, quantile function and random generation for the K-inflated Yule, KIYULE(), distribution.

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

dKIYULE(x, mu = 1, sigma = 0.1, kinf=0, log = FALSE)

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

qKIYULE(p, mu = 1, sigma = 0.1, kinf=0, lower.tail = TRUE, log.p = FALSE)

rKIYULE(n, mu = 1, sigma = 0.1, 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 "logit" link as the default for the sigma parameter
`x`	vector of (non-negative integer) quantiles
`mu`	vector of positive means
`sigma`	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 Yule distribution.

The functions KIYULE return a gamlss.family object which can be used to fit K-inflated Yule 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, KIYULE

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

# gives information about the default links for the  Yule distribution  type II
KIYULE()
#--------------------------------------------------------------------------------

# generate zero inflated Yule distribution
gen.Kinf(family=YULE, kinf=0)

# generate random sample from zero inflated Yule distribution
x<-rinf0YULE(1000,mu=1, sigma=.2)

# fit the zero inflated Yule distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf0YULE, data=data)
histDist(x, family=inf0YULE)
## End(Not run)
#--------------------------------------------------------------------------------

# generated one inflated Yule distribution
gen.Kinf(family=YULE, kinf=1)

# generate random sample from one inflated Yule distribution
x<-rinf1YULE(1000,mu=1, sigma=.2)

# fit the one inflated Yule distribution using gamlss
data<-data.frame(x=x)
## Not run: 
gamlss(x~1, family=inf1YULE, data=data)
histDist(x, family=inf1YULE)
## End(Not run)
#--------------------------------------------------------------------------------

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

#plot the pdf using plot
plot(function(x) dinf1YULE(x, mu=mu, sigma=sigma), 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,pinf1YULE(0:19, mu=mu, sigma=sigma)), 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), qinf1YULE(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 <- rinf1YULE(1000, mu=mu, sigma=sigma)
 hist(Ni,breaks=seq(min(Ni)-0.5,max(Ni)+0.5,by=1),col="lightgray", main="",cex.lab=2)
barplot(table(Ni))
#--------------------------------------------------------------------------------