MOEW: The Marshall-Olkin Extended Weibull (MOEW) distribution

In reliaR: Comprehensive Tools for some Probability Distributions

The Marshall-Olkin Extended Weibull (MOEW) distribution

Description

Density, distribution function, quantile function and random generation for the Marshall-Olkin Extended Weibull (MOEW) distribution with tilt parameter alpha and scale parameter lambda.

Usage

dmoew(x, alpha, lambda, log = FALSE)
pmoew(q, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
qmoew(p, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
rmoew(n, alpha, lambda)

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.
lambda	tilt 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 Marshall-Olkin extended Weibull (MOEW) distribution has density

f(x) = \frac{{\lambda \alpha x^{\alpha - 1} \exp\left({-x^\alpha}\right)}}{{\left\{{1 - (1 - \lambda)\;\exp\left({-x^\alpha}\right)}\right\}^2}};\, x > 0, \lambda > 0, \alpha > 0

where \alpha and \lambda are the tilt and scale parameters, respectively.

Value

dmoew gives the density, pmoew gives the distribution function, qmoew gives the quantile function, and rmoew generates random deviates.

References

Marshall, A. W., Olkin, I. (1997). A new method for adding a parameter to a family of distributions with application to the Weibull and Weibull families. Biometrika,84(3):641-652.

Marshall, A. W., Olkin, I.(2007). Life Distributions: Structure of Nonparametric, Semiparametric, and Parametric Families. Springer, New York.

See Also

.Random.seed about random number; smoew for MOEW survival / hazard etc. functions;

Examples

## Load data sets
data(sys2)
## Maximum Likelihood(ML) Estimates of alpha & lambda for the data(sys2)
## alpha.est = 0.3035937,  lambda.est = 279.2177754

dmoew(sys2, 0.3035937, 279.2177754, log = FALSE)
pmoew(sys2, 0.3035937, 279.2177754, lower.tail = TRUE, log.p = FALSE)
qmoew(0.25, 0.3035937, 279.2177754, lower.tail=TRUE, log.p = FALSE)
rmoew(50, 0.3035937, 279.2177754)

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