Function pgfDlogarithmicpoisson

Description

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

Usage

1

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 logarithmic-Poisson distribution, such that params<-c(theta,lambda), where theta is the probability, lambda is the positive number.

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(.9,7)
pgfDlogarithmicpoisson(.5,params)

## The function is currently defined as

pgfDlogarithmicpoisson <- 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)<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>=1)|(theta<=0))
     stop ("Parameter theta belongs to the interval (0,1)")
if (lambda<=0)
     stop ("Parameter lambda must be positive")
   -lambda*(1-theta)/log(theta)*exp(lambda*(s-1))/(1-(1-theta)*exp(lambda*(s-1)))
}

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