Runuran (version 0.40)

urt: 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.

Author

Josef Leydold and Wolfgang H\"ormann .

Details

The $t$ distribution with df $=\nu$ degrees of freedom has density $$f(x)=\frac{\mathrm{\Gamma }((\nu +1)/2)}{\sqrt{\pi \nu }\mathrm{\Gamma }(\nu /2)}(1+x^2/\nu {)}^{-(\nu +1)/2}$$ 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).

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)