urt function

UNU.RAN Student t random variate generator

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).

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 $= n$ degrees of freedom has density

for all real $x$. It has mean $0$ (for $n > 1$) and variance $n/(n-2)$ (for $n > 2$).

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).

See Also

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

References

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

Author(s)

Josef Leydold and Wolfgang H"ormann unuran@statmath.wu.ac.at .

Note

This function is a wrapper for the UNU.RAN class in . 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.

Examples

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