MOEE: The Marshall-Olkin Extended Exponential (MOEE) distribution
In reliaR: Package for some probability distributions.

Description Usage Arguments Details Value References See Also Examples

Density, distribution function, quantile function and random generation for the Marshall-Olkin Extended Exponential (MOEE) distribution with tilt parameter alpha and scale parameter lambda.

dmoee(x, alpha, lambda, log = FALSE)
pmoee(q, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
qmoee(p, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
rmoee(n, alpha, lambda)

`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`	tilt 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].

The Marshall-Olkin extended exponential (MOEE) distribution has density

f(x; α, λ) = {α λ exp(-λ x)} / {(1 - (1 - α) exp{-λ x})^2}; x > 0, λ > 0, α > 0

where α and λ are the tilt and scale parameters, respectively.

dmoee gives the density, pmoee gives the distribution function, qmoee gives the quantile function, and rmoee generates random deviates.

Marshall, A. W., Olkin, I. (1997). A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika,84(3):641-652.

Marshall, A. W., Olkin, I.(2007). Life Distributions: Structure of Nonparametric, Semiparametric, and Parametric Families. Springer, New York.

.Random.seed about random number; smoee for MOEE survival / hazard etc. functions

## Load data sets
data(stress)
## Estimates of alpha & lambda using 'maxLik' package
## alpha.est = 75.67982, lambda.est = 1.67576
dmoee(stress, 75.67982, 1.67576, log = FALSE)
pmoee(stress, 75.67982, 1.67576, lower.tail = TRUE, 
    log.p = FALSE)
qmoee(0.25, 0.4, 2.0, lower.tail = TRUE, log.p = FALSE)
rmoee(10, 75.67982, 1.67576)