R: The (Modified) PERT Distribution

pert {mc2d} | R Documentation

## The (Modified) PERT Distribution

### Description

Density, distribution function, quantile function and random generation for the PERT (aka Beta PERT) distribution with minimum equals to min, mode equals to mode and maximum equals 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. Default value: 4.
`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 beta distribution extended to the domain [min, max] with mean

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

The underlying beta distribution is specified by shape1 and shape2 defined as

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

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

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

David Vose (See reference) proposed a modified PERT distribution with a shape parameter different from 4.

The PERT distribution is frequently used (with the triangular distribution) to translate expert estimates of the min, max and mode of a random variable in a smooth parametric distribution.

### Value

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

### Author(s)

Regis Pouillot and Matthew Wiener

### References

Vose D. Risk Analysis - A Quantitative Guide (2nd and 3rd editions, John Wiley and Sons, 2000, 2008).

### 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 0.1-18 Index]