pgweibull: Power generalized Weibull distribution

In RTMBdist: Distributions Compatible with Automatic Differentiation by 'RTMB'

Power generalized Weibull distribution

Description

Survival, hazard, cumulative distribution, density, quantile and sampling function for the power generalized Weibull (PgW) distribution with parameters scale, shape and powershape.

Usage

spgweibull(q, scale = 1, shape = 1, powershape = 1, log = FALSE)

hpgweibull(x, scale = 1, shape = 1, powershape = 1, log = FALSE)

ppgweibull(q, scale = 1, shape = 1, powershape = 1,
           lower.tail = TRUE, log.p = FALSE)

dpgweibull(x, scale = 1, shape = 1, powershape = 1, log = FALSE)

qpgweibull(p, scale = 1, shape = 1, powershape = 1)

rpgweibull(n, scale = 1, shape = 1, powershape = 1)

Arguments

scale	positive scale parameter
shape	positive shape parameter
powershape	positive power shape parameter
log, log.p	logical; if TRUE, probabilities/ densities p are returned as \log(p).
x, q	vector of quantiles
lower.tail	logical; if TRUE (default), probabilities are P[X \le x], otherwise P[X > x].
p	vector of probabilities
n	number of observations

Details

The survival function of the PgW distribution is:

S(x) = \exp \left\{ 1 - \left[ 1 + \left(\frac{x}{\theta}\right)^{\nu}\right]^{\frac{1}{\gamma}} \right\}.

The hazard function is

\frac{\nu}{\gamma\theta^{\nu}}\cdot x^{\nu-1}\cdot \left[ 1 + \left(\frac{x}{\theta}\right)^{\nu}\right]^{\frac{1}{\gamma-1}}

The cumulative distribution function is then F(x) = 1 - S(x) and the density function is S(x)\cdot h(x).

If both shape parameters equal 1, the PgW distribution reduces to the exponential distribution (see dexp) with \texttt{rate} = 1/\texttt{scale} If the power shape parameter equals 1, the PgW distribution simplifies to the Weibull distribution (see dweibull) with the same parametrization.

Value

dpgweibull gives the density, ppgweibull gives the distribution function, qpgweibull gives the quantile function, and rpgweibull generates random deviates. spgweibull gives the survival function and hpgweibull gives the hazard function.

Examples

x <- rpgweibull(1, 2, 2, 3)
d <- dpgweibull(x, 2, 2, 3)
p <- ppgweibull(x, 2, 2, 3)
q <- qpgweibull(p, 2, 2, 3)
s <- spgweibull(x, 2, 2, 3)
h <- hpgweibull(x, 2, 2, 3)

RTMBdist documentation built on April 1, 2026, 5:07 p.m.