Compounding (version 1.0.2)

pgfDwaring: Function pgfDwaring

Description

This function calculates value of the pgf's first derivative of the Waring distribution.

Usage

pgfDwaring(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 Waring distribution, such that params<-c(c,a), where $c>a$ and both parameters 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(.8,.4)
pgfDwaring(.5,params)

## The function is currently defined as

pgfDwaring <- 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)<2) 
    stop("At least one value in params is missing")
if (length(params)>2) 
    stop("The length of params is 2")
    cc<-params[1]
    a<-params[2]
if (cc<=0)
    stop ("Parameter c must be positive")
if (a<=0)
    stop ("Parameter a must be positive")

    a*(cc-a)/(cc*(cc+1))*Re(hypergeo(2,a+1,cc+2,s))
}