sod {new.dist}

Standard Omega Distribution

Description

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.

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.

Value

dsod gives the density, psod gives the distribution function, qsod gives the quantile function and rsod generates random deviates.

References

Birbiçer, İ. ve Genç, A. İ., 2022, On parameter estimation of the standard omega distribution. Journal of Applied Statistics, 1-17.

Examples

library(new.dist)
dsod(0.4, alpha=1, beta=2)
psod(0.4, alpha=1, beta=2)
qsod(.8, alpha=1, beta=2)
rsod(10, alpha=1, beta=2)