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.