quagep: Quantile Function of the Generalized Exponential Poisson Distribution

Description

This function computes the quantiles of the Generalized Exponential Poisson distribution given parameters ( $β$ , $κ$ , and $h$ ) of the distribution computed by pargep. The quantile function of the distribution is $x (F) = η^{- 1} \log [1 + h^{- 1} \log (1 - F^{1 / κ} [1 - \exp (- h)])],$ 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

quagep(f, para, paracheck=TRUE)

Value

Quantile value for nonexceedance probability $F$ .

Arguments

f: Nonexceedance probability ( $0 \leq F \leq 1$ ).
para: The parameters from pargep or vec2par.
paracheck: A logical controlling whether the parameters are checked for validity. Overriding of this check might be extremely important and needed for use of the quantile function in the context of TL-moments with nonzero trimming.

Author

W.H. Asquith

Details

If f = 1 or is so close to unity that NaN in the computations of the quantile function, then the function enters into an infinite loop for which an “order of magnitude decrement” on the value of
.Machine$double.eps is made until a numeric hit is encountered. Let $η$ be this machine value, then $F = 1 - η^{1 / j}$ where $j$ is the iteration in the infinite loop. Eventually $F$ becomes small enough that a finite value will result. This result is an estimate of the maximum numerical value the function can produce on the current running platform. This feature assists in the numerical integration of the quantile function for L-moment estimation (see expect.max.ostat). The expect.max.ostat was zealous on reporting errors related to lack of finite integration. However with the “order magnitude decrementing,” then the errors in expect.max.ostat become fewer and are either


Error in integrate(fnb, lower, upper, subdivisions = 200L) : 
  extremely bad integrand behaviour


Error in integrate(fnb, lower, upper, subdivisions = 200L) : 
  maximum number of subdivisions reached

and are shown here to aid in research into Generalized Exponential Power implementation.

References

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

Examples

Run this code

gep <- list(para=c(2, 1.5, 3), type="gep")
quagep(0.5, gep)
if (FALSE) {
  pdf("gep.pdf")
  F <- nonexceeds(f01=TRUE)
  K <- seq(-1,2,by=.2); H <- seq(-1,2,by=.2)
  K <- 10^(K); H <- 10^(H)
  for(i in 1:length(K)) {
    for(j in 1:length(H)) {
      gep <- vec2par(c(2,K[i],H[j]), type="gep")
      message("(K,H): ",K[i]," ",H[j])
      plot(F, quagep(F, gep), lty=i, col=j, type="l", ylim=c(0,4),
           xlab="NONEXCEEDANCE PROBABILITY", ylab="X(F)")
      mtext(paste("(K,H): ",K[i]," ",H[j]))
    }
  }
  dev.off()
}

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