GAT: Generalized Asymmetric t-distribution

In dan9401/st: Asymmetric Student t-Distributions

Generalized Asymmetric t-distribution

Description

Probablity density function(PDF), Cumulative distribution function(CDF), Quantile function and Random generation of the GAT distribution

Usage

dgat(x, mu, scale, alpha, r, c, nu, pars = NULL)

pgat(q, mu, scale, alpha, r, c, nu, pars = NULL)

qgat(p, mu, scale, alpha, r, c, nu, pars = NULL)

rgat(n, mu, scale, alpha, r, c, nu, pars = NULL)

Arguments

x, q	vector of quantiles
mu	location parameter
scale	scale parameter, scale > 0
alpha	how early tail behavior is apparent, alpha > 0
r	tail power asymmetry, r > 0
c	scale asymmetry, c > 0
nu	degrees of freedom / tail parameter, nu > 0
pars	a vector that contains mu, scale, alpha, r, c, nu, if pars is specified, mu, scale, alpha, r, c, nu should not be specified
p	vector of probablilities
n	number of observations for random generation

Value

dgat gives the density, pgat gives the distribution function, qgat gives the quantile function, and rgat generates random samples for GATdistribution.

References

Baker, R. D. (2016). A new asymmetric generalisation of the t-distribution. arXiv preprint arXiv:1606.05203. \Sexpr[results=rd]{tools:::Rd_expr_doi("https://doi.org/10.48550/arXiv.1606.05203")}

Examples

dgat(0, 0.12, 0.6, 1.5, 1.2, 2, 5)
pgat(0.12, 0.12, 0.6, 1.5, 1.2, 2, 5)
qgat(0.4, 0.12, 0.6, 1.5, 1.2, 2, 5)
data = rgat(1000, 0.12, 0.6, 1.5, 1.2, 2, 5)
hist(data, breaks = 50, probability = TRUE)

# using the 'pars' argument
pars <- c(0.12, 0.6, 1.5, 1.2, 2, 5)
x <- seq(-3, 3, 0.01)
y <- dgat(x, pars = pars)
lines(x, y, col = 4)

dan9401/st documentation built on Jan. 6, 2025, 8:28 p.m.