ExpExt: The Exponential Extension(EE) distribution

In reliaR: Comprehensive Tools for some Probability Distributions

The Exponential Extension(EE) distribution

Description

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

Usage

dexp.ext(x, alpha, lambda, log = FALSE)
pexp.ext(q, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
qexp.ext(p, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
rexp.ext(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 \le x] otherwise, P[X > x].

Details

The Exponential Extension(EE) distribution has density

f(x) = \alpha \lambda \left(1+\lambda x\right)^{\alpha -1} \exp \left\{1-\left(1+\lambda x\right)^{\alpha } \right\} ;\, x\ge 0, \alpha >0, \lambda >0.

where \alpha and \lambda are the shape and scale parameters, respectively.

Value

dexp.ext gives the density, pexp.ext gives the distribution function, qexp.ext gives the quantile function, and rexp.ext generates random deviates.

References

Nikulin, M. and Haghighi, F. (2006). A Chi-squared test for the generalized power Weibull family for the head-and-neck cancer censored data, Journal of Mathematical Sciences, Vol. 133(3), 1333-1341.

See Also

.Random.seed about random number; sexp.ext for ExpExt survival / hazard etc. functions

Examples

## Load data sets
data(sys2)
## Maximum Likelihood(ML) Estimates of alpha & lambda for the data(sys2)
## Estimates of alpha & lambda using 'maxLik' package
## alpha.est = 1.0126e+01, lambda.est = 1.5848e-04
dexp.ext(sys2, 1.012556e+01, 1.5848e-04, log = FALSE)
pexp.ext(sys2, 1.012556e+01, 1.5848e-04, lower.tail = TRUE, log.p = FALSE)
qexp.ext(0.25, 1.012556e+01, 1.5848e-04, lower.tail=TRUE, log.p = FALSE)
rexp.ext(30, 1.012556e+01, 1.5848e-04)

reliaR documentation built on Nov. 5, 2025, 6:57 p.m.