Probability Density Function of the Generalized Exponential Poisson Distribution

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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.

Author(s)

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.

See Also

pdfgep, quagep, lmomgep, pargep

Examples

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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)

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