Generalized Weibull Distribution

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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

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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(s)

J.K. Lindsey

See Also

dweibull for the Weibull distribution, df for the F distribution, dburr for the Burr distribution.

Examples

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

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