ExpoLogistic: The Exponentiated Logistic(EL) distribution

In reliaR: Package for some probability distributions.

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 ≤ x] otherwise, P[X > x].

Details

The Exponentiated Logistic(EL) distribution has density

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

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

Value

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

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)

reliaR documentation built on May 1, 2019, 9:51 p.m.