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 $$x>0,~\alpha \in \left( 0,1\right]. $$