pdftri: Probability Density Function of the Asymmetric Triangular...

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

Probability Density Function of the Asymmetric Triangular Distribution

Description

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

f(x) = \frac{2(x-\nu)}{(\omega - \nu)(\psi - \nu)}\mbox{,}

for x < \omega,

f(x) = \frac{2(\psi-x)}{(\psi - \omega)(\psi - \nu)}\mbox{,}

for x > \omega, and

f(x) = \frac{2}{(\psi - \nu)}\mbox{,}

for x = \omega 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.

Usage

pdftri(x, para)

Arguments

x	A real value vector.
para	The parameters from partri or vec2par.

Value

Probability density (f) for x.

Author(s)

W.H. Asquith

See Also

pdftri, quatri, lmomtri, partri

Examples

  tri <- vec2par(c(-120, 102, 320), type="tri")
  x <- quatri(nonexceeds(),tri)
  pdftri(x,tri)

wasquith/lmomco documentation built on April 10, 2024, 4:20 a.m.