urchisq {Runuran}

UNU.RAN Chi-Squared random variate generator

Description

UNU.RAN random variate generator for the Chi-Squared (\chi^2) distribution with df degrees of freedom. It also allows sampling from the truncated distribution.

[Special Generator] – Sampling Function: Chi-squared.

Usage

urchisq(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.

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

Note

This function is wrapper for the UNU.RAN class in R. Compared to rchisq, urchisq is faster, especially for larger sample sizes. However, in opposition to rchisq vector arguments are ignored, i.e. only the first entry is used.

Author(s)

Josef Leydold and Wolfgang H\"ormann [e-mail].

References

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

See Also

runif and .Random.seed about random number generation, unuran for the UNU.RAN class, and rchisq for the R built-in generator.

Examples

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