new.dist (version 0.1.1)

sgrd: 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)

Value

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

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

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)