Compounding (version 1.0.2)

pgfDyule: Function pgfDyule

Description

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

Usage

pgfDyule(s, params)

Arguments

s

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

params

Postive parameter of the Yule distribution, such that params<-theta.

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<-.3
pgfDyule(.5,params)

## The function is currently defined as
pgfDyule <- 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)>1) 
    stop("The length of params is 1")
    theta<-params[1]
if (theta<=0)
    stop ("Parameter theta must be positive")

    theta/((theta+1)*(theta+2))*Re(hypergeo(2,2,theta+3,s))
}