GenExp: The Generalized Exponential (GE) distribution

In reliaR: Package for some probability distributions.

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)

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 generalized exponential distribution has density

f(x; α, λ) = α λ x 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

dgen.exp gives the density, pgen.exp gives the distribution function, qgen.exp gives the quantile function, and rgen.exp 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. (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)

Example output

 [1] 0.0028085519 0.0079037993 0.0096302793 0.0121772720 0.0122952977
 [6] 0.0128219891 0.0130808408 0.0131462640 0.0131455392 0.0130930394
[11] 0.0130191482 0.0114874649 0.0113424824 0.0113424824 0.0113004906
[16] 0.0084137777 0.0067868385 0.0058880089 0.0049450364 0.0048479045
[21] 0.0025569374 0.0025477360 0.0006209358
 [1] 0.01286358 0.07155254 0.10741060 0.20144342 0.20878560 0.25256674
 [7] 0.29406620 0.33397324 0.33555075 0.36390160 0.38270591 0.53404257
[13] 0.54363137 0.54363137 0.54634853 0.69681369 0.76508716 0.80003070
[19] 0.83506297 0.83858833 0.91801056 0.91831684 0.98062023
[1] 45.39964
 [1] 56.01547 63.18654 50.72547 53.41902 55.47022 63.29746 55.77808 57.20096
 [9] 34.72875 59.88666

reliaR documentation built on May 1, 2019, 9:51 p.m.