Create UNU.RAN object for a Student t distribution with
with df degrees of freedom.
[Distribution] -- t (Student).
Usage
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.
Value
An object of class "unuran.cont".
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 domain of the distribution can be truncated to the
interval (lb,ub).
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.
## Create distribution object for t distributiondistr <- udt(df=4)
## Generate generator object; use method PINV (inversion)gen <- pinvd.new(distr)
## Draw a sample of size 100x <- ur(gen,100)