Description Usage Arguments Details Value Author(s) References See Also Examples

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.

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`x,q` |
Vector of quantiles. |

`p` |
Vector of probabilities. |

`n` |
Number of observations. If length(n) |

`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]. |

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.

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

Regis Pouillot and Matthew Wiener

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

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mc2d documentation built on May 30, 2017, 6:30 a.m.

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