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.
Value
dsgrd gives the density, psgrd gives the distribution
function, qsgrd gives the quantile function and rsgrd generates
random deviates.
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)
#> [1] 0.08314235
psgrd(5,theta=3,alpha=1,beta=4)
#> [1] 0.9989333
qsgrd(.4,theta=3,alpha=1,beta=4)
#> [1] 0.8358487
rsgrd(10,theta=3,alpha=1,beta=4)
#> [1] 0.8661765 0.7299448 1.2136410 1.2759740 1.1884832 0.6049862 0.6922031
#> [8] 0.8057631 0.8001224 0.5925698