Density, distribution function, quantile function and random generation for the Standard Omega distribution.
Usage
dsod(x, alpha, beta, log = FALSE)
psod(q, alpha, beta, lower.tail = TRUE, log.p = FALSE)
qsod(p, alpha, beta, lower.tail = TRUE)
rsod(n, alpha, beta)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.
Value
dsod gives the density, psod gives the distribution
function, qsod gives the quantile function and rsod generates
random deviates.
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 $$0<x<1,~\alpha ,\beta >0.$$