# pgfDpascalpoisson: Function pgfDpascalpoisson In Compounding: Computing Continuous Distributions

## Description

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

## Usage

 `1` ```pgfDpascalpoisson(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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25``` ```params<-c(3,2,.5) pgfDpascalpoisson(.5,params) ## The function is currently defined as pgfDpascalpoisson <- 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 mu<-params a<-params 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") mu*exp(theta*(s-1))*(1+mu/(a*theta)-mu/(a*theta)*exp(theta*(s-1)))^(-a-1) } ```

Compounding documentation built on May 2, 2019, 1:04 p.m.