skewt (version 1.0)

SkTDist: The Skewed Student t Distribution

Description

Density, distribution function, quantile function and random generation for the skewed t distribution, as introduced by Fernandez and Steel, with df degrees of freedom.

Usage

dskt(x, df, gamma = 1)
pskt(x, df, gamma = 1)
qskt(p, df, gamma)
rskt(n, df, gamma)

Arguments

x

vector of quantiles.

p

vector of probabilities.

n

number of observations. If length(n) > 1, the length is taken to be the number required.

df

degrees of freedom (\(> 0\), maybe non-integer).

gamma

skewing parameter, \(\gamma\)

Value

dskt gives the density, pskt gives the distribution function, qskt gives the quantile function, and rskt generates random deviates.

Details

The Skewed \(t\) distribution with df \(= \nu\) degrees of freedom has the following density, where \(f(x)\) is the density of the \(t\) distribution, with \(= \nu\) degrees of freedom : $$f(x) = \frac{2}{\gamma + \frac{1}{\gamma}} f(\gamma x) \quad for \quad x<0$$ and $$f(x) = \frac{2}{\gamma + \frac{1}{\gamma}} f(\frac{x}{\gamma}) \quad for \quad x \ge 0$$

References

Fernandez, C. and Steel, M. F. J. (1998). On Bayesian modeling of fat tails and skewness, J. Am. Statist. Assoc. 93, 359--371.

Rohr, P. and Hoeschele, I. (2002). Bayesian QTL mapping using skewed Student-\(t\) distributions, Genet. Sel. Evol. 34, 1--21.

See Also

df for the F distribution.

Examples

# NOT RUN {
dskt(0.5,2)
dskt(0.01,2,2)
pskt(1.25,2,2)
pskt(c(0.5,1.25),3)
qskt(c(0,0.025,0.25,0.5,0.75,0.975,1),2,2)
rskt(100,2,2)
plot(function(x)dskt(x,2,2),-3,3,n=301)
# }