Compounding (version 1.0.2)

pgfDneymantypeb: Function pgfDneymantypeb

Description

This function calculates value of the pgf's first derivative of the Neyman type B distribution.

Usage

pgfDneymantypeb(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 Neyman type B distribution, such that params<-c(theta,lambda), where both parameters are positive numbers.

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(4,5)
pgfDneymantypeb(.5,params)


## The function is currently defined as

pgfDneymantypeb <- 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")
    theta<-params[1]
    lambda<-params[2]
if (theta<=0)
    stop ("Parameter theta must be positive")
if (lambda<=0)
    stop ("Parameter lambda must be positive")
    theta*lambda/2*genhypergeo(2,3,theta*(s-1))*pgfneymantypeb(s,params)
}