cdftri: Cumulative Distribution Function of the Asymmetric Triangular... In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

Description

This function computes the cumulative probability or nonexceedance probability of the Asymmetric Triangular distribution given parameters (ν, ω, and ψ) computed by partri. The cumulative distribution function is

F(x) = \frac{(x - ν)^2}{(ω-ν)(ψ-ν)}\mbox{,}

for x < ω,

F(x) = 1 - \frac{(ψ - x)^2}{(ψ - ω)(ψ - ν)}\mbox{,}

for x > ω, and

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

for x = ω 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.

Usage

 1 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

pdftri, quatri, lmomtri, partri
 1 2  lmr <- lmoms(c(46, 70, 59, 36, 71, 48, 46, 63, 35, 52)) cdftri(50,partri(lmr))