dST: The skewed t distribution

In betategarch: Simulation, Estimation and Forecasting of Beta-Skew-t-EGARCH Models

The skewed t distribution

Description

Density, random number generation, mean, variance, skewness and kurtosis functions for the uncentred skewed t distribution. The skewing method is that of Fernandez and Steel (1998).

Usage

dST(y, df = 10, sd = 1, skew = 1, log = FALSE)
rST(n, df = 10, skew = 1)
STmean(df, skew = 1)
STvar(df, skew = 1)
STskewness(df, skew = 1)
STkurtosis(df, skew = 1)

Arguments

y	numeric vector of quantiles
n	integer, the number of observations
df	degrees of freedom, greater than 0 and less than Inf
sd	scale, greater than 0 and less than Inf
skew	skewness, greater than 0 and less than Inf. Symmetry obtains when skew = 1 (default).
log	logical. TRUE returns the natural log of the density value, FALSE (default) returns the density value.

Details

Empty

Value

dST:	a numeric value, either the density value or the natural log of the density value
rST:	a numeric vector with n random numbers
STmean:	The mean of an uncentred skewed t variable
STvar:	The variance of an uncentred skewed t variable
STskewness:	3rd. moment of a standardised skewed t variable
STkurtosis:	4th. moment of a standardised skewed t variable

Note

Empty

Author(s)

Genaro Sucarrat, https://www.sucarrat.net/

References

C. Fernandez and M. Steel (1998), 'On Bayesian Modeling of Fat Tails and Skewness', Journal of the American Statistical Association 93, pp. 359-371, \Sexpr[results=rd]{tools:::Rd_expr_doi("https://doi.org/10.1080/01621459.1998.10474117")}

See Also

tegarchSim

Examples

##generate 1000 random numbers from the skewed t:
set.seed(123)
eps <- rST(500, df=5) #symmetric t
eps <- rST(500, df=5, skew=0.8) #skewed to the left
eps <- rST(500, df=5, skew=2) #skewed to the right

##compare empirical mean with analytical:
mean(eps)
STmean(5, skew=2)

##compare empirical variance with analytical:
var(eps)
STvar(5, skew=2)

betategarch documentation built on April 3, 2025, 9:54 p.m.