UNU.RAN random variate generator for the F distribution with
with df1 and df2 degrees of freedom.
It also allows sampling from the truncated distribution.
[Special Generator] -- Sampling Function: F.
Usage
urf(n, df1, df2, lb=0, ub=Inf)
Arguments
n
size of required sample.
df1, df2
(strictly positive) degrees of freedom. Non-integer
values allowed.
The F distribution with df1 = \(n_1\) and df2 =
\(n_2\) degrees of freedom has density
$$
f(x) = \frac{\Gamma(n_1/2 + n_2/2)}{\Gamma(n_1/2)\Gamma(n_2/2)}
\left(\frac{n_1}{n_2}\right)^{n_1/2} x^{n_1/2 -1}
\left(1 + \frac{n_1 x}{n_2}\right)^{-(n_1 + n_2) / 2}%
$$
for \(x > 0\).
The generation algorithm uses fast numerical inversion. The parameters
lb and ub can be used to generate variates from
the F 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
rf for the R built-in generator.