sgrd: Slashed Generalized Rayleigh Distribution

In new.dist: Alternative Continuous and Discrete Distributions

Slashed Generalized Rayleigh Distribution

Description

Density, distribution function, quantile function and random generation for the Slashed generalized Rayleigh distribution with parameters shape, scale and kurtosis.

Usage

dsgrd(x, theta, alpha, beta, log = FALSE)

psgrd(q, theta, alpha, beta, lower.tail = TRUE, log.p = FALSE)

qsgrd(p, theta, alpha, beta, lower.tail = TRUE)

rsgrd(n, theta, alpha, beta)

Arguments

x, q	vector of quantiles.
theta	a scale parameter.
alpha	a shape parameter.
beta	a kurtosis 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 Slashed Generalized Rayleigh distribution with shape parameter \alpha, scale parameter \theta and kurtosis parameter \beta, has density

f\left( x\right) =\frac{\beta x^{-\left( \beta+1\right)}}{\Gamma \left( \alpha+1\right) \theta ^{\beta/2}}\Gamma \left( \frac{2\alpha +\beta +2}{2} \right)F\left( \theta x^{2};\frac{2\alpha +\beta +2}{2},1\right),

where F(.;a,b) is the cdf of the Gamma (a,b) distribution, and

x>0,~\theta >0,~\alpha >-1~and~\beta >0

Value

dsgrd gives the density, psgrd gives the distribution function, qsgrd gives the quantile function and rsgrd generates random deviates.

References

Iriarte, Y. A., Vilca, F., Varela, H. ve Gómez, H. W., 2017, Slashed generalized Rayleigh distribution, Communications in Statistics- Theory and Methods, 46 (10), 4686-4699.

Examples

library(new.dist)
dsgrd(2,theta=3,alpha=1,beta=4)
psgrd(5,theta=3,alpha=1,beta=4)
qsgrd(.4,theta=3,alpha=1,beta=4)
rsgrd(10,theta=3,alpha=1,beta=4)

new.dist documentation built on May 29, 2024, 3:40 a.m.