Density, distribution function, quantile function and random generation for the EP distribution.
Usage
dEPd(x, lambda, beta, log = FALSE)
pEPd(q, lambda, beta, lower.tail = TRUE, log.p = FALSE)
qEPd(p, lambda, beta, lower.tail = TRUE)
rEPd(n, lambda, beta)Arguments
- x, q
vector of quantiles.
- lambda, beta
are parameters.
- log, log.p
logical; if TRUE, probabilities p are given as log(p).
- lower.tail
logical; if TRUE (default), probabilities are \(P\left[ X\leq x\right]\), otherwise, \(P\left[ X>x\right] \).
- p
vector of probabilities.
- n
number of observations. If
length(n) > 1, the length is taken to be the number required.
Value
dEPd gives the density, pEPd gives the distribution
function, qEPd gives the quantile function and rEPd generates
random deviates.
Details
The EP distribution with parameters \(\lambda\) and \(\beta\), has density $$f\left( x\right) =\frac{\lambda \beta } {\left( 1-e^{-\lambda }\right) } e^{-\lambda -\beta x+\lambda e^{-\beta x}},$$ where $$x>\mathbb{R}_{+},~\beta ,\lambda \in \mathbb{R}_{+}.$$
References
Kuş, C., 2007, A new lifetime distribution, Computational Statistics & Data Analysis, 51 (9), 4497-4509.