# 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

## See Also

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

## Examples

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