udt function

UNU.RAN object for Student t distribution

Create UNU.RAN object for a Student t distribution with with df degrees of freedom.

[Distribution] -- t (Student).

udt(df, lb=-Inf, ub=Inf)

Arguments

• df: degrees of freedom (strictly positive). Non-integer values allowed.
• 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 domain of the distribution can be truncated to the interval (lb,ub).

Returns

An object of class "unuran.cont".

See Also

unuran.cont.

References

N.L. Johnson, S. Kotz, and N. Balakrishnan (1995): Continuous Univariate Distributions, Volume 2. 2nd edition, John Wiley & Sons, Inc., New York. Chap. 28, p. 362.

Author(s)

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

Examples

## Create distribution object for t distribution
distr <- udt(df=4)
## Generate generator object; use method PINV (inversion)
gen <- pinvd.new(distr)
## Draw a sample of size 100
x <- ur(gen,100)