quatri: Quantile Function of the Asymmetric Triangular Distribution

In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

Quantile Function of the Asymmetric Triangular Distribution

Description

This function computes the quantiles of the Asymmetric Triangular distribution given parameters (\nu, \omega, and \psi) of the distribution computed by partri. The quantile function of the distribution is

x(F) = \nu + \sqrt{(\psi - \nu)(\omega - \nu)F}\mbox{,}

for F < P,

x(F) = \psi - \sqrt{(\psi - \nu)(\psi - \omega)(1-F)}\mbox{,}

for F > P, and

x(F) = \omega\mbox{,}

for F = P where x(F) is the quantile for nonexceedance probability F, \nu is the minimum, \psi is the maximum, and \omega is the mode of the distribution and

P = \frac{(\omega - \nu)}{(\psi - \nu)}\mbox{.}

Usage

quatri(f, para, paracheck=TRUE)

Arguments

f	Nonexceedance probability (0 \le F \le 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

See Also

cdftri, pdftri, lmomtri, partri

Examples

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

lmomco documentation built on Aug. 30, 2023, 5:10 p.m.