reliaR (version 0.2)

ExpExt: 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)

Value

dexp.ext gives the density,

pexp.ext gives the distribution function,

qexp.ext gives the quantile function, and

rexp.ext 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 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.

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)