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)
Value
domd gives the density, pomd gives the distribution
function, qomd gives the quantile function and romd generates
random deviates.
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.
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
$$x>0,~\alpha \in \left( 0,1\right]. $$
References
Jodrá, P., Jiménez-Gamero, M. D. ve Alba-Fernández, M. V., 2015,
On the Muth distribution, Mathematical Modelling and Analysis, 20 (3),
291-310.