GPWeibull: The generalized power Weibull(GPW) distribution

In reliaR: Comprehensive Tools for some Probability Distributions

The generalized power Weibull(GPW) distribution

Description

Density, distribution function, quantile function and random generation for the generalized power Weibull(GPW) distribution with shape parameters alpha and theta.

Usage

dgp.weibull(x, alpha, theta, log = FALSE)
pgp.weibull(q, alpha, theta, lower.tail = TRUE, log.p = FALSE)
qgp.weibull(p, alpha, theta, lower.tail = TRUE, log.p = FALSE)
rgp.weibull(n, alpha, theta)

Arguments

x, q	vector of quantiles.
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.
alpha	shape parameter.
theta	shape parameter.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are P[X \le x] otherwise, P[X > x].

Details

The generalized power Weibull(GPW) distribution has density

f(x) = \alpha \theta x^{\alpha -1} \left(1 + x^{\alpha} \right)^{\theta - 1} \exp\left\{1-\left(1+x^{\alpha}\right)^{\theta}\right\};\, x \ge 0, \alpha > 0, \theta > 0.

where \alpha and \theta are the shape and scale parameters, respectively.

Value

dgp.weibull gives the density, pgp.weibull gives the distribution function, qgp.weibull gives the quantile function, and rgp.weibull generates random deviates.

References

Nikulin, M. and Haghighi, F. (2006). A Chi-squared test for the generalized power Weibull family for the head-and-neck cancer censored data, Journal of Mathematical Sciences, Vol. 133(3), 1333-1341.

Pham, H. and Lai, C.D. (2007). On recent generalizations of the Weibull distribution, IEEE Trans. on Reliability, Vol. 56(3), 454-458.

See Also

.Random.seed about random number; sgp.weibull for generalized power Weibull(GPW) survival / hazard etc. functions

Examples

## Load data sets
data(repairtimes)
## Maximum Likelihood(ML) Estimates of alpha & theta for the data(repairtimes)
## Estimates of alpha & theta using 'maxLik' package
## alpha.est = 1.566093, theta.est = 0.355321

dgp.weibull(repairtimes, 1.566093, 0.355321, log = FALSE)
pgp.weibull(repairtimes, 1.566093, 0.355321, lower.tail = TRUE, log.p = FALSE)
qgp.weibull(0.25, 1.566093, 0.355321, lower.tail=TRUE, log.p = FALSE)
rgp.weibull(30, 1.566093, 0.355321)

reliaR documentation built on Nov. 5, 2025, 6:57 p.m.