Density, distribution function, quantile function and random generation for on the Muth distribution.
Usage
domd(x, alpha, log = FALSE)
pomd(q, alpha, lower.tail = TRUE, log.p = FALSE)
qomd(p, alpha, lower.tail = TRUE)
romd(n, alpha)Arguments
- x, q
vector of quantiles.
- alpha
a parameter.
- 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
domd gives the density, pomd gives the distribution
function, qomd gives the quantile function and romd generates
random deviates.
Details
The Muth distribution with a parameter \(\alpha\), has density $$f\left( x\right) =\left( e^{\alpha x}- \alpha \right) e^{\alpha x-\left(1/\alpha \right) \left( e^{\alpha x}- 1\right) },$$ where $$x>0,~\alpha \in \left( 0,1\right]. $$