Runuran (version 0.40)

udchisq: UNU.RAN object for Chi-Squared distribution

Description

Create UNU.RAN object for a Chi-squared (\(\chi^2\)) distribution with df degrees of freedom.

[Distribution] -- Chi-squared.

Usage

udchisq(df, lb=0, ub=Inf)

Value

An object of class "unuran.cont".

Arguments

df

degrees of freedom (strictly positive). 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 Chi-squared distribution with df\(= n > 0\) degrees of freedom has density $$ f_n(x) = \frac{1}{{2}^{n/2} \Gamma (n/2)} {x}^{n/2-1} {e}^{-x/2} $$ 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 (1994): Continuous Univariate Distributions, Volume 1. 2nd edition, John Wiley & Sons, Inc., New York. Chap. 18, p. 416

See Also

unuran.cont.

Examples

## Create distribution object for chi-squared distribution
distr <- udchisq(df=5)
## Generate generator object; use method PINV (inversion)
gen <- pinvd.new(distr)
## Draw a sample of size 100
x <- ur(gen,100)