urf: UNU.RAN F random variate generator

In Runuran: R Interface to the 'UNU.RAN' Random Variate Generators

UNU.RAN F random variate generator

Description

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.
lb	lower bound of (truncated) distribution.
ub	upper bound of (truncated) distribution.

Details

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).

Note

This function is wrapper for the UNU.RAN class in R. Compared to rf, urf is faster, especially for larger sample sizes. However, in opposition to rf vector arguments are ignored, i.e. only the first entry is used.

Author(s)

Josef Leydold and Wolfgang H\"ormann [e-mail].

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.

Examples

## Create a sample of size 1000
x <- urf(n=1000,df1=3,df2=5)

Runuran documentation built on April 12, 2025, 1:35 a.m.