Cumulative Distribution Function of the Asymmetric Triangular Distribution

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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

See Also

pdftri, quatri, lmomtri, partri

Examples

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

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