Runuran (version 0.40)

udf: UNU.RAN object for F distribution

Description

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

[Distribution] -- F.

Usage

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

Value

An object of class "unuran.cont".

Arguments

df1, df2

(strictly positive) degrees of freedom. Non-integer values allowed.

lb

lower bound of (truncated) distribution.

ub

upper bound of (truncated) distribution.

Author

Josef Leydold and Wolfgang H\"ormann .

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 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. 27, p. 332

See Also

unuran.cont.

Examples

## 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)