# quatexp: Quantile Function of the Truncated Exponential Distribution In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

## Description

This function computes the quantiles of the Truncated Exponential distribution given parameters (ψ and α) computed by partexp. The parameter ψ is the right truncation, and α is a scale parameter. The quantile function, letting β = 1/α to match nomenclature of Vogel and others (2008), is

x(F) = -\frac{1}{β}\log(1-F[1-\mathrm{exp}(-βψ)])\mbox{,}

where x(F) is the quantile 0 ≤ x ≤ ψ for nonexceedance probability F and ψ > 0 and α > 0. This distribution represents a nonstationary Poisson process.

The distribution is restricted to a narrow range of L-CV (τ_2 = λ_2/λ_1). If τ_2 = 1/3, the process represented is a stationary Poisson for which the quantile function is simply the uniform distribution and x(F) = ψ\,F. If τ_2 = 1/2, then the distribution is represented as the usual exponential distribution with a location parameter of zero and a scale parameter 1/β. Both of these limiting conditions are supported.

## Usage

 1 quatexp(f, para, paracheck=TRUE) 

## Arguments

 f Nonexceedance probability (0 ≤ F ≤ 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.

## Value

Quantile value for nonexceedance probability F.

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.

cdftexp, pdftexp, lmomtexp, partexp

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 lmr <- vec2lmom(c(40,0.38), lscale=FALSE) quatexp(0.5,partexp(lmr)) ## Not run: 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)) } ## End(Not run) 

### Example output

[1] 36.79779


lmomco documentation built on Sept. 21, 2018, 6:40 p.m.