# WeibullExt: The Weibull Extension(WE) distribution In reliaR: Package for some probability distributions.

## Description

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

## Usage

 ```1 2 3 4``` ```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 ≤ x] otherwise, P[X > x].

## Details

The Weibull Extension(WE) distribution has density

f(x; α, β) = β (x/α)^{β - 1} exp(x/α)^β exp{-α(exp(x/α)^β - 1)}; (α, c β) > 0, x > 0

where α and β are the `shape` and `scale` parameters, respectively.

## Value

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

## 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

 ``` 1 2 3 4 5 6 7 8 9 10``` ```## 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) ```

reliaR documentation built on May 29, 2017, 12:34 p.m.