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
(or, alternatively, mean equals to mean) and maximum equals to max.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | ```
dpert(x, min = -1, mode = 0, max = 1, shape = 4, log = FALSE, mean = 0)
ppert(
q,
min = -1,
mode = 0,
max = 1,
shape = 4,
lower.tail = TRUE,
log.p = FALSE,
mean = 0
)
qpert(
p,
min = -1,
mode = 0,
max = 1,
shape = 4,
lower.tail = TRUE,
log.p = FALSE,
mean = 0
)
rpert(n, min = -1, mode = 0, max = 1, shape = 4, mean = 0)
``` |

`x, q` |
Vector of quantiles. |

`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). |

`mean` |
Vector of means, can be specified in place of mode as an alternative parametrization. |

`lower.tail` |
Logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x] |

`p` |
Vector of probabilities |

`n` |
Number of observations. If length(n) > 1, the length is taken to be the number required. |

The PERT distribution is a `Beta`

distribution extended to the domain [min, max] with mean

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

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

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

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

mode or mean can be specified, but not both. Note: mean is the last parameter for back-compatibility. A warning will be provided if some combinations of min, mean and max leads to impossible mode.

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).

1 2 3 4 5 6 7 8 | ```
curve(dpert(x,min=3,mode=5,max=10,shape=6), from = 2, to = 11, lty=3,ylab="density")
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 = .30, c("Default: 4","shape: 2","shape: 6"), lty=1:3)
## Alternatie parametrization using mean
curve(dpert(x,min=3,mean=5,max=10), from = 2, to = 11, lty=2 ,ylab="density")
curve(dpert(x,min=3,mode=5,max=10), from = 2, to = 11, add=TRUE)
legend(x = 8, y = .30, c("mode: 5","mean: 5"), lty=1:2)
``` |

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