FlexWeibull: The flexible Weibull(FW) distribution

In reliaR: Comprehensive Tools for some Probability Distributions

The flexible Weibull(FW) distribution

Description

Density, distribution function, quantile function and random generation for the flexible Weibull(FW) distribution with parameters alpha and beta.

Usage

dflex.weibull(x, alpha, beta, log = FALSE)
pflex.weibull(q, alpha, beta, lower.tail = TRUE, log.p = FALSE)
qflex.weibull(p, alpha, beta, lower.tail = TRUE, log.p = FALSE)
rflex.weibull(n, alpha, beta)

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	parameter.
beta	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 flexible Weibull(FW) distribution has density

f(x) = \left(\alpha + \frac{\beta}{x^2}\right) \exp\left(\alpha \, x - \frac{\beta}{x}\right)\, \exp\left\{-\exp\left(\alpha x - \frac{\beta}{x}\right)\right\};\, x \ge 0, \alpha > 0, \beta > 0.

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

Value

dflex.weibull gives the density, pflex.weibull gives the distribution function, qflex.weibull gives the quantile function, and rflex.weibull generates random deviates.

References

Bebbington, M., Lai, C.D. and Zitikis, R. (2007). A flexible Weibull extension, Reliability Engineering and System Safety, 92, 719-726.

See Also

.Random.seed about random number; sflex.weibull for flexible Weibull(FW) survival / hazard etc. functions

Examples

## Load data sets
data(repairtimes)
## Maximum Likelihood(ML) Estimates of alpha & beta for the data(repairtimes)
## Estimates of alpha & beta using 'maxLik' package
## alpha.est = 0.07077507, beta.est = 1.13181535

dflex.weibull(repairtimes, 0.07077507, 1.13181535, log = FALSE)
pflex.weibull(repairtimes, 0.07077507, 1.13181535, lower.tail = TRUE, log.p = FALSE)
qflex.weibull(0.25, 0.07077507, 1.13181535, lower.tail=TRUE, log.p = FALSE)
rflex.weibull(30, 0.07077507, 1.13181535)

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