reliaR (version 0.01)

MOEE: The Marshall-Olkin Extended Exponential (MOEE) distribution

Description

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

Usage

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)

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

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 $P[X \le x]$ otherwise, $P[X > x]$.

Value

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

Details

The Marshall-Olkin extended exponential (MOEE) distribution has density $$f(x; \alpha, \lambda) = \frac{\alpha \lambda e^{-\lambda x}}{\left\{1-(1-\alpha) e^{-\lambda x} \right\}^2};\, x > 0, \lambda > 0, \alpha > 0$$ where $\alpha$ and $\lambda$ are the tilt and scale parameters, respectively.

References

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.

See Also

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

Examples

## 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)