Runuran (version 0.40)

urchi: UNU.RAN Chi random variate generator

Description

UNU.RAN random variate generator for the Chi (\(\chi\)) distribution with df degrees of freedom. It also allows sampling from the truncated distribution. (Do not confuse with the Chi-Squared (\(\chi^2\)) distribution!)

[Special Generator] -- Sampling Function: Chi.

Usage

urchi(n, df, lb=0, ub=Inf)

Arguments

n

size of required sample.

df

degrees of freedom (strictly positive, but can be non-integer).

lb

lower bound of (truncated) distribution.

ub

upper bound of (truncated) distribution.

Author

Josef Leydold and Wolfgang H\"ormann .

Details

The Chi distribution with df\(= n > 0\) degrees of freedom has density $$ f(x) = x^{n-1} e^{-x^2/2} $$ for \(x > 0\).

The generation algorithm uses fast numerical inversion. The parameters lb and ub can be used to generate variates from the Chi distribution truncated to the interval (lb,ub).

References

W. H\"ormann, J. Leydold, and G. Derflinger (2004): Automatic Nonuniform Random Variate Generation. Springer-Verlag, Berlin Heidelberg

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.417.

See Also

runif and .Random.seed about random number generation and unuran for the UNU.RAN class.

Examples

## Create a sample of size 1000
x <- urchi(n=1000,df=3)