# udf: UNU.RAN object for F distribution In Runuran: R Interface to the UNU.RAN Random Variate Generators

## Description

Create UNU.RAN object for an F distribution with mean with `df1` and `df2` degrees of freedom.

[Distribution] – F.

## Usage

 `1` ```udf(df1, df2, lb=0, ub=Inf) ```

## Arguments

 `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 =` n1 and `df2 =` n2 degrees of freedom has density

f(x) = Gamma((n1 + n2)/2) / (Gamma(n1/2) Gamma(n2/2)) * (n1/n2)^(n1/2) x^(n1/2 - 1) * (1 + (n1/n2) x)^(-(n1 + n2)/2)

for x > 0.

The domain of the distribution can be truncated to the interval (`lb`,`ub`).

## Value

An object of class `"unuran.cont"`.

## Author(s)

Josef Leydold and Wolfgang H\"ormann [email protected].

## References

N.L. Johnson, S. Kotz, and N. Balakrishnan (1995): Continuous Univariate Distributions, Volume 2. 2nd edition, John Wiley & Sons, Inc., New York. Chap. 27, p. 332

`unuran.cont`.
 ```1 2 3 4 5 6``` ```## Create distribution object for F distribution distr <- udf(df1=3,df2=6) ## Generate generator object; use method PINV (inversion) gen <- pinvd.new(distr) ## Draw a sample of size 100 x <- ur(gen,100) ```