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

 1 2 3 4 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