# InvGenExp: The Inverse Generalized Exponential(IGE) distribution In reliaR: Package for some probability distributions.

## Description

Density, distribution function, quantile function and random generation for the Inverse Generalized Exponential(IGE) distribution with shape parameter `alpha` and scale parameter `lambda`.

## Usage

 ```1 2 3 4``` ```dinv.genexp(x, alpha, lambda, log = FALSE) pinv.genexp(q, alpha, lambda, lower.tail = TRUE, log.p = FALSE) qinv.genexp(p, alpha, lambda, lower.tail = TRUE, log.p = FALSE) rinv.genexp(n, alpha, lambda) ```

## 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. `lambda` 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 Inverse Generalized Exponential(IGE) distribution has density

f(x; α, λ) = (α λ)/x^2 exp{-λ/x} {1 - exp{-λ/x}}^{α - 1}; (α, λ) > 0, x > 0

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

## Value

`dinv.genexp` gives the density, `pinv.genexp` gives the distribution function, `qinv.genexp` gives the quantile function, and `rinv.genexp` generates random deviates.

## References

Gupta, R. D. and Kundu, D. (2001). Exponentiated exponential family; an alternative to gamma and Weibull distributions, Biometrical Journal, 43(1), 117-130.

Gupta, R.D. and Kundu, D. (2007). Generalized exponential distribution: Existing results and some recent development, Journal of Statistical Planning and Inference. 137, 3537-3547.

`.Random.seed` about random number; `sinv.genexp` for Inverse Generalized Exponential(IGE) survival / hazard etc. functions
 ```1 2 3 4 5 6 7 8 9``` ```## Load data sets data(repairtimes) ## Maximum Likelihood(ML) Estimates of alpha & lambda for the data(repairtimes) ## Estimates of alpha & lambda using 'maxLik' package ## alpha.est = 1.097807, lambda.est = 1.206889 dinv.genexp(repairtimes, 1.097807, 1.206889, log = FALSE) pinv.genexp(repairtimes, 1.097807, 1.206889, lower.tail = TRUE, log.p = FALSE) qinv.genexp(0.25, 1.097807, 1.206889, lower.tail=TRUE, log.p = FALSE) rinv.genexp(30, 1.097807, 1.206889) ```