reliaR (version 0.2)

InvGenExp: The Inverse Generalized Exponential(IGE) distribution

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

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)

Value

dinv.genexp gives the density,

pinv.genexp gives the distribution function,

qinv.genexp gives the quantile function, and

rinv.genexp generates random deviates.

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 \(P[X \le x]\) otherwise, \(P[X > x]\).

Details

The Inverse Generalized Exponential(IGE) distribution has density $$f(x; \alpha, \lambda) = \frac{\alpha \; \lambda}{x^2}\; e^{-\lambda /x} \; \left\{1-e^{-\lambda /x}\right\}^{\alpha - 1};\; (\alpha, \lambda) > 0, x > 0$$ where \(\alpha\) and \(\lambda\) are the shape and scale parameters, respectively.

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.

See Also

.Random.seed about random number; sinv.genexp for Inverse Generalized Exponential(IGE) survival / hazard etc. functions

Examples

## 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)