lmomco (version 2.4.14)

quatexp: Quantile Function of the Truncated Exponential Distribution

Description

This function computes the quantiles of the Truncated Exponential distribution given parameters (\(\psi\) and \(\alpha\)) computed by partexp. The parameter \(\psi\) is the right truncation, and \(\alpha\) is a scale parameter. The quantile function, letting \(\beta = 1/\alpha\) to match nomenclature of Vogel and others (2008), is $$x(F) = -\frac{1}{\beta}\log(1-F[1-\mathrm{exp}(-\beta\psi)])\mbox{,}$$ where \(x(F)\) is the quantile \(0 \le x \le \psi\) for nonexceedance probability \(F\) and \(\psi > 0\) and \(\alpha > 0\). This distribution represents a nonstationary Poisson process.

The distribution is restricted to a narrow range of L-CV (\(\tau_2 = \lambda_2/\lambda_1\)). If \(\tau_2 = 1/3\), the process represented is a stationary Poisson for which the quantile function is simply the uniform distribution and \(x(F) = \psi\,F\). If \(\tau_2 = 1/2\), then the distribution is represented as the usual exponential distribution with a location parameter of zero and a scale parameter \(1/\beta\). Both of these limiting conditions are supported.

Usage

quatexp(f, para, paracheck=TRUE)

Value

Quantile value for nonexceedance probability \(F\).

Arguments

f

Nonexceedance probability (\(0 \le F \le 1\)).

para

The parameters from partexp 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

References

Vogel, R.M., Hosking, J.R.M., Elphick, C.S., Roberts, D.L., and Reed, J.M., 2008, Goodness of fit of probability distributions for sightings as species approach extinction: Bulletin of Mathematical Biology, DOI 10.1007/s11538-008-9377-3, 19 p.

See Also

cdftexp, pdftexp, lmomtexp, partexp

Examples

lmr <- vec2lmom(c(40,0.38), lscale=FALSE)
quatexp(0.5,partexp(lmr))
if (FALSE) {
F <- seq(0,1,by=0.001)
A <- partexp(vec2lmom(c(100, 1/2), lscale=FALSE))
plot(qnorm(F), quatexp(F, A), pch=16, type='l')
by <- 0.01; lcvs <- c(1/3, seq(1/3+by, 1/2-by, by=by), 1/2)
reds <- (lcvs - 1/3)/max(lcvs - 1/3)
for(lcv in lcvs) {
    A <- partexp(vec2lmom(c(100, lcv), lscale=FALSE))
    lines(qnorm(F), quatexp(F, A), col=rgb(reds[lcvs == lcv],0,0))
}
}