reliaR (version 0.2)

GenExp: The Generalized Exponential (GE) distribution

Description

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

Usage

dgen.exp(x, alpha, lambda, log = FALSE)
pgen.exp(q, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
qgen.exp(p, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
rgen.exp(n, alpha, lambda)

Value

dgen.exp gives the density,

pgen.exp gives the distribution function,

qgen.exp gives the quantile function, and

rgen.exp 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 generalized exponential distribution has density $$f(x; \alpha, \lambda) = \alpha \lambda x\; e^{-\lambda x} \; \left\{1-e^{-\lambda x} \right\}^{\alpha -1};\; (\alpha, \lambda) > 0, x > 0.$$ 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. (1999). Generalized exponential distributions. Australian and New Zealand Journal of Statistics, 41(2), 173 - 188.

See Also

.Random.seed about random number; sgen.exp for GE survival / hazard etc. functions

Examples

## Load data set
data(bearings)
## Estimates of alpha & lambda using 'maxLik' package
## alpha.est = 5.28321139, lambda.est = 0.03229609

dgen.exp(bearings, 5.28321139, 0.03229609, log = FALSE)
pgen.exp(bearings, 5.28321139, 0.03229609, lower.tail = TRUE, 
    log.p = FALSE)
qgen.exp(0.25, 5.28321139, 0.03229609, lower.tail = TRUE, log.p = FALSE)
rgen.exp(10, 5.28321139, 0.03229609)