jfst {neodistr} | R Documentation |
Jones Faddy's Skew-t Distribution
Description
To calculate density function, distribution funcion, quantile function, and build data from random generator function for the Jones-Faddy's Skew-t Distribution.
Usage
djfst(x, mu = 0, sigma = 1, alpha = 2, beta = 2, log = FALSE)
pjfst(
q,
mu = 0,
sigma = 1,
alpha = 2,
beta = 2,
lower.tail = TRUE,
log.p = FALSE
)
qjfst(
p,
mu = 0,
sigma = 1,
alpha = 2,
beta = 2,
lower.tail = TRUE,
log.p = FALSE
)
rjfst(n, mu = 0, sigma = 1, alpha = 2, beta = 2)
Arguments
x , q |
vector of quantiles. |
mu |
a location parameter. |
sigma |
a scale parameter. |
alpha |
a shape parameter (skewness). |
beta |
a shape parameter (kurtosis). |
log , log.p |
logical; if TRUE, probabilities p are given as log(p) The default value of this parameter is FALSE |
lower.tail |
logical;if TRUE (default), probabilities are
|
p |
vectors of probabilities. |
n |
number of observations. |
Details
Jones-Faddy's Skew-t Distribution
The Jones-Faddy's Skew-t distribution with parameters \mu
, \sigma
,\alpha
, and \beta
has density:
f(x |\mu,\sigma,\beta,\alpha)= \frac{c}{\sigma} {\left[{1+\frac{z}{\sqrt{\alpha+\beta+z^2}}}\right]}^{\alpha+\frac{1}{2}}
{\left[{1-\frac{z}{\sqrt{\alpha+\beta+z^2}}}\right]}^{\beta+\frac{1}{2}}
where -\infty<x<\infty, -\infty<\mu<\infty, \sigma>0, \alpha>0, \beta>0,
z =\frac{x-\mu}{\sigma}
, c = {\left[2^{\left(\alpha+\beta-1\right)} {\left(\alpha+\beta\right)^{\frac{1}{2}}} B(a,b)\right]}^{-1}
,
Value
djfst
gives the density , pjfst
gives the distribution function,
qjfst
gives quantiles function, rjfst
generates random numbers.
Author(s)
Anisa' Faoziah
References
Jones, M.C. and Faddy, M. J. (2003) A skew extension of the t distribution, with applications. Journal of the Royal Statistical Society, Series B, 65, pp 159-174
Rigby, R.A. and Stasinopoulos, M.D. and Heller, G.Z. and De Bastiani, F. (2019) Distributions for Modeling Location, Scale, and Shape: Using GAMLSS in R.CRC Press
Examples
djfst(4, mu=0, sigma=1, alpha=2, beta=2)
pjfst(4, mu=0, sigma=1, alpha=2, beta=2)
qjfst(0.4, mu=0, sigma=1, alpha=2, beta=2)
r=rjfst(10000, mu=0, sigma=1, alpha=2, beta=2)
head(r)
hist(r, xlab = 'jfst random number', ylab = 'Frequency',
main = 'Distribution of jfst Random Number ')