pert {mc2d}R Documentation

The Pert Distribution

Description

Density, distribution function, quantile function and random generation for the pert distribution with minimum equal to min, mode equal to mode and maximum equal to max.

Usage

dpert(x, min=-1, mode=0, max=1, shape=4, log=FALSE)
ppert(q, min=-1, mode=0, max=1, shape=4, lower.tail=TRUE, log.p=FALSE)
qpert(p, min=-1, mode=0, max=1, shape=4, lower.tail=TRUE, log.p=FALSE)
rpert(n, min=-1, mode=0, max=1, shape=4)

Arguments

x,q Vector of quantiles.
p Vector of probabilities.
n Number of observations. If length(n) > 1, the length is taken to be the number required.
min Vector of minima.
mode Vector of modes.
max Vector of maxima.
shape Vector of scaling parameters.
log, log.p Logical; if TRUE, probabilities p are given as log(p).
lower.tail Logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x].

Details

The Pert distribution is a special case of the Beta distribution specified by the following parameters. Given:

mu = (min + max + shape * mode)/(shape + 2)

the values of shape1 and shape2 are

shape1=(mu - min)*(2 mode-min-max)/((mode-mu)*(max - min)

shape2=shape1*(max - mu)/(mu - min)

on the domain [min, max].

If mu=mode, shape1 is set to 1+shape/2.

Value

dpert gives the density, ppert gives the distribution function, qpert gives the quantile function, and rpert generates random deviates.

Author(s)

Regis Pouillot

References

Vose D. Risk Analysis - A Quantitative Guide (John Wiley & Sons, 2000).

See Also

Beta

Examples

curve(dpert(x, min=3, mode=5, max=10, shape=6), from = 2, to = 11, lty=3)
curve(dpert(x, min=3, mode=5, max=10), from = 2, to = 11, add=TRUE)
curve(dpert(x, min=3, mode=5, max=10, shape=2), from = 2, to = 11, add=TRUE, lty=2)
legend(x = 8, y = 2, c("Default", "shape:2", "shape:6"), lty=1:3)



[Package mc2d version 0.1-5 Index]