udchisq function

UNU.RAN object for Chi-Squared distribution

UNU.RAN object for Chi-Squared distribution

Create UNU.RAN object for a Chi-squared (chi2chi^2) distribution with df degrees of freedom.

[Distribution] -- Chi-squared.

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

Arguments

  • df: degrees of freedom (strictly positive). Non-integer values allowed.
  • lb: lower bound of (truncated) distribution.
  • ub: upper bound of (truncated) distribution.

Details

The Chi-squared distribution with df=n>0= n > 0 degrees of freedom has density

fn(x)=12n/2Γ(n/2)xn/21ex/2fn(x)=1/(2(n/2)Gamma(n/2))x(n/21)e(x/2) f_n(x) = \frac{1}{{2}^{n/2} \Gamma (n/2)} {x}^{n/2-1} {e}^{-x/2}f_n(x) = 1 / (2^(n/2) Gamma(n/2)) x^(n/2-1) e^(-x/2)

for x>0x > 0.

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

Returns

An object of class "unuran.cont".

See Also

unuran.cont.

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

Author(s)

Josef Leydold and Wolfgang H"ormann unuran@statmath.wu.ac.at .

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)
  • Maintainer: Josef Leydold
  • License: GPL (>= 2)
  • Last published: 2025-04-07