# quatri: Quantile Function of the Asymmetric Triangular Distribution In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

## Description

This function computes the quantiles of the Asymmetric Triangular distribution given parameters (ν, ω, and ψ) of the distribution computed by partri. The quantile function of the distribution is

x(F) = ν + √{(ψ - ν)(ω - ν)F}\mbox{,}

for F < P,

x(F) = ψ - √{(ψ - ν)(ψ - ω)(1-F)}\mbox{,}

for F > P, and

x(F) = ω\mbox{,}

for F = P where x(F) is the quantile for nonexceedance probability F, ν is the minimum, ψ is the maximum, and ω is the mode of the distribution and

P = \frac{(ω - ν)}{(ψ - ν)}\mbox{.}

## Usage

 1 quatri(f, para, paracheck=TRUE) 

## Arguments

 f Nonexceedance probability (0 ≤ F ≤ 1). para The parameters from partri 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.

## Author(s)

W.H. Asquith

cdftri, pdftri, lmomtri, partri
 1 2  lmr <- lmoms(c(46, 70, 59, 36, 71, 48, 46, 63, 35, 52)) quatri(0.5,partri(lmr))