dsod gives the density, psod gives the distribution
function, qsod gives the quantile function and rsod generates
random deviates.
Arguments
x, q
vector of quantiles.
alpha, 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.
Details
The Standard Omega distribution with parameters
\(\alpha\) and \(\beta\), has density
$$f\left( x\right) =\alpha \beta x^{\beta -1}\frac{1}{1-x^{2\beta }}
\left( \frac{1+x^{\beta }}{1-x^{\beta }}\right) ^{-\alpha /2},$$
where
$$0<x<1,~\alpha ,\beta >0.$$
References
Birbiçer, İ. ve Genç, A. İ., 2022,
On parameter estimation of the standard omega distribution. Journal of
Applied Statistics, 1-17.