urt {Runuran}

UNU.RAN Student t random variate generator

Description

UNU.RAN random variate generator for the Student t distribution with with df degrees of freedom. It also allows sampling from the truncated distribution.

[Special Generator] – Sampling Function: t (Student).

Usage

urt(n, df, lb = -Inf, ub = Inf)

Arguments

n

size of required sample.

df

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

lb

lower bound of (truncated) distribution.

ub

upper bound of (truncated) distribution.

Details

The t distribution with df = \nu degrees of freedom has density

f(x) = \frac{\Gamma ((\nu+1)/2)}{\sqrt{\pi \nu} \Gamma (\nu/2)} (1 + x^2/\nu)^{-(\nu+1)/2}%

for all real x. It has mean 0 (for \nu > 1) and variance \frac{\nu}{\nu-2} (for \nu > 2).

The generation algorithm uses fast numerical inversion. The parameters lb and ub can be used to generate variates from the t distribution truncated to the interval (lb,ub).

Note

This function is a wrapper for the UNU.RAN class in R. Compared to rt, urt is faster, especially for larger sample sizes. However, in opposition to rt vector arguments are ignored, i.e. only the first entry is used.

Author(s)

Josef Leydold and Wolfgang H\"ormann [e-mail].

References

W. H\"ormann, J. Leydold, and G. Derflinger (2004): Automatic Nonuniform Random Variate Generation. Springer-Verlag, Berlin Heidelberg

See Also

runif and .Random.seed about random number generation, unuran for the UNU.RAN class, and rt for the R built-in generator.

Examples

## Create a sample of size 1000
x <- urt(n=1000,df=4)