cdftri {lmomco}

Cumulative Distribution Function of the Asymmetric Triangular Distribution

Description

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

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

for x < \omega,

F(x) = 1 - \frac{(\psi - x)^2}{(\psi - \omega)(\psi - \nu)}\mbox{,}

for x > \omega, and

F(x) = \frac{(\omega - \nu)}{(\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

cdftri(x, para)

Arguments

x

A real value vector.

para

The parameters from partri or vec2par.

Value

Nonexceedance probability (F) for x.

Author(s)

W.H. Asquith

See Also

pdftri, quatri, lmomtri, partri

Examples

  lmr <- lmoms(c(46, 70, 59, 36, 71, 48, 46, 63, 35, 52))
  cdftri(50,partri(lmr))