Function pgfIpascalpoisson

Description

This function calculates value of the pgf's inverse of the Pascal Poisson distribution.

Usage

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pgfIpascalpoisson(s, params)

Arguments

s

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

params

List of the parameters of the Pascal Poisson distribution, such that params<-c(theta,mu, a), where all parameters are positive.

Author(s)

S. Nadarajah, B. V. Popovic, M. M. Ristic

References

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

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

Examples

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params<-c(3,2,.5)
pgfIpascalpoisson(.9,params)


## The function is currently defined as

pgfIpascalpoisson <- function(s,params) {
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)<3) 
    stop("At least one value in params is missing")
if (length(params)>3) 
    stop("The length of params is 3")
    theta<-params[1]
    mu<-params[2]
    a<-params[3]
if (theta<=0)
    stop ("Parameter theta must be positive")
if (mu<=0)
    stop ("Parameter mu must be positive")
if (a<=0)
    stop ("Parameter a must be positive")
    zval<-1+mu/(a*theta)-s^(-1/a)
    1+log(a*theta*zval/mu)/theta
}

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