reliaR (version 0.01)

ExpoLogistic: The Exponentiated Logistic(EL) distribution

Description

Density, distribution function, quantile function and random generation for the Exponentiated Logistic(EL) distribution with shape parameter alpha and scale parameter beta.

Usage

dexpo.logistic(x, alpha, beta, log = FALSE)
pexpo.logistic(q, alpha, beta, lower.tail = TRUE, log.p = FALSE)
qexpo.logistic(p, alpha, beta, lower.tail = TRUE, log.p = FALSE)
rexpo.logistic(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

dexpo.logistic gives the density, pexpo.logistic gives the distribution function, qexpo.logistic gives the quantile function, and rexpo.logistic generates random deviates.

Details

The Exponentiated Logistic(EL) distribution has density $$f(x; \alpha, \beta) = \frac{\alpha}{\beta} \exp\left(-\frac{x}{\beta}\right)\left\{1+\exp\left(-\frac{x}{\beta}\right)\right\}^{-(\alpha + 1)};\; (\alpha, \beta) > 0, x > 0$$

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

References

Ali, M.M., Pal, M. and Woo, J. (2007). Some Exponentiated Distributions, The Korean Communications in Statistics, 14(1), 93-109.

Shirke, D.T., Kumbhar, R.R. and Kundu, D. (2005). Tolerance intervals for exponentiated scale family of distributions, Journal of Applied Statistics, 32, 1067-1074

See Also

.Random.seed about random number; sexpo.logistic for Exponentiated Logistic(EL) survival / hazard etc. functions

Examples

## Load data sets
data(dataset2)
## Maximum Likelihood(ML) Estimates of alpha & beta for the data(dataset2)
## Estimates of alpha & beta using 'maxLik' package
## alpha.est = 5.31302, beta.est = 139.04515

dexpo.logistic(dataset2, 5.31302, 139.04515, log = FALSE)
pexpo.logistic(dataset2, 5.31302, 139.04515, lower.tail = TRUE, log.p = FALSE)
qexpo.logistic(0.25, 5.31302, 139.04515, lower.tail=TRUE, log.p = FALSE)
rexpo.logistic(30, 5.31302, 139.04515)