UnivRNG (version 1.2.3)

draw.noncentral.chisquared: Generates variates from non-central chi-squared distribution

Description

This function implements pseudo-random number generation for a non-central chi-squared distribution with pdf

$$f(x|\lambda,\nu)=\frac{e^{-(x+\lambda)/2}x^{\nu/2-1}}{2^{\nu/2}} \sum_{k=0}^{\infty} \frac{(\lambda x)^{k}}{4^{k}k!\Gamma(k+\nu/2)}$$

for \(0 \leq x < \infty\), \(\lambda>0\), and \(\nu>1\), where \(\lambda\) is the non-centrality parameter and \(\nu\) is the degrees of freedom.

Usage

draw.noncentral.chisquared(nrep,dof,ncp)

Arguments

nrep

Number of data points to generate.

dof

Degrees of freedom of the desired non-central chi-squared distribution.

ncp

Non-centrality parameter of the desired non-central chi-squared distribution.

Value

A list of length five containing generated data, the theoretical mean, the empirical mean, the theoretical variance, and the empirical variance with names y, theo.mean, emp.mean, theo.var, and emp.var, respectively.

Examples

# NOT RUN {
draw.noncentral.chisquared(nrep=100000,dof=2,ncp=1)

draw.noncentral.chisquared(nrep=100000,dof=5,ncp=2)
# }