lmomco (version 2.3.1)

cdfgep: Cumulative Distribution Function of the Generalized Exponential Poisson Distribution

Description

This function computes the cumulative probability or nonexceedance probability of the Generalized Exponential Poisson distribution given parameters (\(\beta\), \(\kappa\), and \(h\)) computed by pargep. The cumulative distribution function is $$F(x) = \left(\frac{1 - \exp[-h + h\exp(-\eta x)]}{1 - \exp(-h)}\right)^\kappa\mbox{,}$$ 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

cdfgep(x, para)

Arguments

x

A real value vector.

para

The parameters from pargep or vec2par.

Value

Nonexceedance probability (\(F\)) 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 {
gep <- list(para=c(2, 1.5, 3), type="gep")
cdfgep(0.48,gep)
# }