rmutil (version 1.1.10)

Generalized Weibull: 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 $$f(y)=\frac{\sigma \nu y^{\sigma -1}(1-\exp (-(y/\mu {)}^{\sigma }){)}^{\nu -1}\exp (-(y/\mu {)}^{\sigma })}{{\mu }^{\sigma }}$$

where $\mu$ is the scale parameter of the distribution, $\sigma$ is the shape, and $\nu$ is the family parameter.

$\nu =1$ gives a Weibull distribution, for $\sigma =1$, $\nu <0$ a generalized F distribution, and for $\sigma >0$, $\nu \le 0$ a Burr type XII distribution.

Usage

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

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)