reliaR (version 0.01)

WeibullExt: The Weibull Extension(WE) distribution

Description

Density, distribution function, quantile function and random generation for the Weibull Extension(WE) distribution with shape parameter alpha and scale parameter beta.

Usage

dweibull.ext(x, alpha, beta, log = FALSE)
pweibull.ext(q, alpha, beta, lower.tail = TRUE, log.p = FALSE)
qweibull.ext(p, alpha, beta, lower.tail = TRUE, log.p = FALSE)
rweibull.ext(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

shape parameter.

beta

scale 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, $P[X > x]$.

Value

dweibull.ext gives the density, pweibull.ext gives the distribution function, qweibull.ext gives the quantile function, and rweibull.ext generates random deviates.

Details

The Weibull Extension(WE) distribution has density $$f(x; \alpha, \beta) = \beta \left(\frac{x}{\alpha}\right)^{\beta - 1} \exp\left(\frac{x}{\alpha}\right)^{\beta}\; \exp\left\{-\alpha\;\left(\exp\left(\frac{x}{\alpha}\right)^{\beta} - 1\right)\right\};\; (\alpha, c \beta) > 0, x > 0$$ where $\alpha$ and $\beta$ are the shape and scale parameters, respectively.

References

Murthy, D.N.P., Xie, M. and Jiang, R. (2003). Weibull Models, Wiley, New York

Tang, Y., Xie, M. and Goh, T.N., (2003). Statistical analysis of a Weibull extension model, Communications in Statistics: Theory & Methods 32(5):913-928.

Xie, M., Tang, Y., Goh, T.N., (2002). A modified Weibull extension with bathtub-shaped failure rate function, Reliability Engineering System Safety 76(3):279-285.

Zhang, T., and Xie, M.(2007). Failure Data Analysis with Extended Weibull Distribution, Communications in Statistics-Simulation and Computation, 36(3), 579-592.

See Also

.Random.seed about random number; sweibull.ext for Weibull Extension(WE) survival / hazard etc. functions

Examples

## Load data sets
data(sys2)
## Maximum Likelihood(ML) Estimates of alpha & beta for the data(sys2)
## Estimates of alpha & beta using 'maxLik' package
## alpha.est = 0.00019114, beta.est = 0.14696242

dweibull.ext(sys2, 0.00019114, 0.14696242, log = FALSE)
pweibull.ext(sys2, 0.00019114, 0.14696242, lower.tail = TRUE, log.p = FALSE)
qweibull.ext(0.25, 0.00019114, 0.14696242, lower.tail=TRUE, log.p = FALSE)
rweibull.ext(30, 0.00019114, 0.14696242)