lmomco (version 2.3.1)

pdfgep: Probability Density Function of the Generalized Exponential Poisson Distribution

Description

This function computes the probability density of the Generalized Exponential Poisson distribution given parameters (\(\beta\), \(\kappa\), and \(h\)) computed by pargep. The probability density function is $$f(x) = \frac{\kappa h \eta}{[1 - \exp(-h)]^\kappa}{1 - \exp[-h + h\exp(-\eta x)}\times\exp[-h - \eta x + h\exp(-\eta x)]\mbox{,}$$ where \(F(x)\) is the nonexceedance probability for quantile \(x > 0\), \(\eta = 1/\beta\), \(\beta > 0\) is a scale parameter, \(\kappa > 0\) is a shape parameter, and \(h > 0\) is another shape parameter.

Usage

pdfgep(x, para)

Arguments

x

A real value vector.

para

The parameters from pargep or vec2par.

Value

Probability density (\(f\)) for \(x\).

References

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

See Also

pdfgep, quagep, lmomgep, pargep

Examples

# NOT RUN {
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)
}
# }