# pdfgep: Probability Density Function of the Generalized Exponential... In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

## Description

This function computes the probability density of the Generalized Exponential Poisson distribution given parameters (β, κ, and h) computed by pargep. The probability density function is

f(x) = \frac{κ h η}{[1 - \exp(-h)]^κ}{1 - \exp[-h + h\exp(-η x)}\times\exp[-h - η x + h\exp(-η x)]\mbox{,}

where F(x) is the nonexceedance probability for quantile x > 0, η = 1/β, β > 0 is a scale parameter, κ > 0 is a shape parameter, and h > 0 is another shape parameter.

## Usage

 1 pdfgep(x, para) 

## Arguments

 x A real value vector. para The parameters from pargep or vec2par.

## Value

Probability density (f) for x.

W.H. Asquith

## References

Barreto-Souza, W., and Cribari-Neto, F., 2009, A generalization of the exponential-Poisson distribution: Statistics and Probability, 79, pp. 2493–2500.

pdfgep, quagep, lmomgep, pargep
  1 2 3 4 5 6 7 8 9 10 11 pdfgep(0.5, vec2par(c(10,2.9,1.5), type="gep")) ## Not run: x <- seq(0,3, by=0.01); ylim <- c(0,1.5) plot(NA,NA, xlim=range(x), ylim=ylim, xlab="x", ylab="f(x)") mtext("Barreto-Souza and Cribari-Neto (2009, fig. 1)") K <- c(0.1, 1, 5, 10) for(i in 1:length(K)) { gep <- vec2par(c(2,K[i],1), type="gep"); lines(x, pdfgep(x, gep), lty=i) } ## End(Not run)