# pgfDyule: Function pgfDyule In Compounding: Computing Continuous Distributions

## Description

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

## Usage

 `1` ```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.

## 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

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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```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)) } ```

Compounding documentation built on May 30, 2017, 4:02 a.m.