Compounding (version 1.0.2)

pgfDkattitypeh2: Function pgfDkattitypeh2

Description

This function calculates value of the pgf's derivative of the Katti type H2 distribution.

Usage

pgfDkattitypeh2(s, params)

Arguments

s

Value of the parameter of the pgf. It should be from interval [-1,1]. In the opposite pgf diverges.

params

List of the parameters of the Katti type H2 distribution, such that params<-c(theta,a,b,k), where all parameter are positive.

References

Johnson N, Kotz S, Kemp A (1992) Univariate Discrete Distributions, John Wiley and Sons, New York

Hankin R.K.S, Lee A (2006) A new family of non-negative distributions. Australia and New Zealand Journal of Statistics 48(1): 67(78)

http://www.am.qub.ac.uk/users/g.gribakin/sor/Chap3.pdf

Examples

params<-c(.4,9,5,7)
pgfDkattitypeh2(.5,params)


## The function is currently defined as

pgfDkattitypeh2 <- function(s,params) {
    require(hypergeo)
k<-s[abs(s)>1]
if (length(k)>0)
    warning("At least one element of the vector s are out of interval [-1,1]")
if (length(params)<4) 
   stop("At least one value in params is missing")
if (length(params)>4) 
   stop("The length of params is 4")
    theta<-params[1]
    a<-params[2]
    b<-params[3]
    k<-params[4]
if (theta<=0)
  stop ("Parameter theta must be positive")
if (a<=0)
  stop ("Parameter a must be positive")
if (b<=0)
  stop ("Parameter b must be positive")
if (k<=0)
  stop ("Parameter k must be positive")    
a*k*theta/(a+b)*Re(hypergeo(k+1,a+1,a+b+1,theta*(s-1)))
}