# pgfDkattitypeh2: Function pgfDkattitypeh2 In Compounding: Computing Continuous Distributions

## Description

This function calculates value of the pgf's derivative of the Katti type H2 distribution.

## Usage

 `1` ```pgfDkattitypeh2(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 Katti type H2 distribution, such that params<-c(theta,a,b,k), where all parameter 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

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 18 19 20 21 22 23 24 25 26 27 28 29``` ```params<-c(.4,9,5,7) pgfDkattitypeh2(.5,params) ## The function is currently defined as pgfDkattitypeh2 <- 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)<4) stop("At least one value in params is missing") if (length(params)>4) stop("The length of params is 4") theta<-params a<-params b<-params k<-params if (theta<=0) stop ("Parameter theta must be positive") if (a<=0) stop ("Parameter a must be positive") if (b<=0) stop ("Parameter b must be positive") if (k<=0) stop ("Parameter k must be positive") a*k*theta/(a+b)*Re(hypergeo(k+1,a+1,a+b+1,theta*(s-1))) } ```

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