GExp: Generalized Exponential Distribution
In aneisse/survdistr: Survival Analysis Distributions

Description Usage Arguments Details Value Author(s) Source References See Also Examples

Density, distribution function, quantile function and random generation for the GExp distribution with parameters alpha, lambda and mu.

dgexp(x, alpha, lambda, mu, log = FALSE)

pgexp(q, alpha, lambda, mu, lower.tail = TRUE, log.p = FALSE)

qgexp(p, alpha, lambda, mu, lower.tail = TRUE, log.p = FALSE)

rgexp(n, alpha, lambda, mu, cens.prop = 0)

`x, q`	numeric vector of quantiles. x > μ.
`alpha`	shape parameter α > 0.
`lambda`	shape parameter λ > 0.
`mu`	location parameter μ < x.
`log, log.p`	logical; if `TRUE`, probabilities/densities `p` are given as `log(p)`.
`lower.tail`	logical; if `TRUE`, probabilities are P[X ≤ x], otherwise, P[X ≥ x]
`n`	desired size of the random number sample.
`cens.prop`	proportion of censored data to be simulated. If greater than `0`, a matrix will be returned instead of a vector. The matrix will contain the random values and a censorship indicator variable.

The GExp distribution has density

f(x) = (α/λ)(1-e^(-(x-μ)/λ))^(α-1)e^(-(x-μ)/λ)

with shape parameter α, scale parameter λ and location parameter μ and x > μ as described by Gupta and Kundu (1999).

With alpha = 1 GExp equals the Two-parameter Exponential distribution with rate = 1/lambda. Such dsitribution can be computed by a Exponential transforming the variable g(x) = x - mu.

With alpha = 1 and mu = 0 GExp equals the usual Exponential distribution.

dgexp gives the density, pgexp gives the distribution function, qgexp gives the quantile function, and rgexp generates random values.

The length of the result is determined by n for rgexp, for the other fucntions the length is the same as the vector passed to the first argument.

Only the first element of the logical arguments are used.

Anderson Neisse <a.neisse@gmail.com>

The source code of all distributions in this package can also be found on the survdistr Github repository.

GUPTA, R. D.; KUNDU, D. Theory & methods: Generalized exponential distributions. Australian & New Zealand Journal of Statistics, 1999, 41.2: 173-188.

LAWLESS, J. F. Prediction intervals for the two parameter exponential distribution. Technometrics, 1977, 19.4: 469-472.

LINK TO OTHER PACKAGE DISTRIBUTIONS

# Equivalency with the Two-parameter Exponential distribution
all.equal(dgexp(5, alpha = 1, lambda = 2, mu = 3),
          dexp(5 - 3, rate = 1/2))

# Equivalency with the exponential distribution
all.equal(dgexp(5, alpha = 1, lambda = 2, mu = 0),
          dexp(5, rate = 1/2))

# Generating values and comparing with the function
x <- rgexp(10000, alpha = 1.5, lambda = 2, mu = 3)
hist(x, probability = T, ylim = c(0, 0.5), breaks = 100)
curve(dgexp(x, alpha = 1.5, lambda = 2, mu = 3),
      from = 0, to = 25, add = T)