Generalized Weibull {rmutil} | R Documentation |

## Generalized Weibull Distribution

### Description

These functions provide information about the generalized Weibull
distribution, also called the exponentiated Weibull, with scale
parameter equal to `m`

, shape equal to `s`

, and family
parameter equal to `f`

: density, cumulative distribution,
quantiles, log hazard, and random generation.

The generalized Weibull distribution has density

*f(y) = s f y^(s-1) (1-exp(-(y/m)^s))^(f-1) exp(-(y/m)^s)/m^s*

where *m* is the scale parameter of the distribution,
*s* is the shape, and *f* is the family
parameter.

*f=1* gives a Weibull distribution, for
*s=1*, *f<0* a generalized F distribution,
and for *s>0*, *f<=0* a Burr type XII distribution.

### Usage

dgweibull(y, s, m, f, log=FALSE)
pgweibull(q, s, m, f)
qgweibull(p, s, m, f)
hgweibull(y, s, m, f)
rgweibull(n, s, m, f)

### Arguments

`y` |
vector of responses. |

`q` |
vector of quantiles. |

`p` |
vector of probabilities |

`n` |
number of values to generate |

`m` |
vector of location parameters. |

`s` |
vector of dispersion parameters. |

`f` |
vector of family parameters. |

`log` |
if TRUE, log probabilities are supplied. |

### Author(s)

J.K. Lindsey

### See Also

`dweibull`

for the Weibull distribution,
`df`

for the F distribution,
`dburr`

for the Burr distribution.

### Examples

dgweibull(5, 1, 3, 2)
pgweibull(5, 1, 3, 2)
qgweibull(0.65, 1, 3, 2)
rgweibull(10, 1, 3, 2)

[Package

*rmutil* version 1.0

Index]