simEd (version 2.0.0)

vchisq: Variate Generation for Chi-Squared Distribution

Description

Variate Generation for Chi-Squared Distribution

Usage

vchisq(n, df, ncp = 0, stream = NULL, antithetic = FALSE, asList = FALSE)

Arguments

n

number of observations

df

Degrees of freedom (non-negative, but can be non-integer)

ncp

Non-centrality parameter (non-negative)

stream

if NULL (default), uses stats::runif to generate uniform variates to invert via stats::qchisq; otherwise, an integer in 1:25 indicates the rstream stream from which to generate uniform variates to invert via stats::qchisq;

antithetic

if FALSE (default), inverts $u$ = uniform(0,1) variate(s) generated via either stats::runif or rstream::rstream.sample; otherwise, uses $1-u$

asList

if FALSE (default), output only the generated random variates; otherwise, return a list with components suitable for visualizing inversion. See return for details

Value

If asList is FALSE (default), return a vector of random variates.

Otherwise, return a list with components suitable for visualizing inversion, specifically:

u

A vector of generated U(0,1) variates

x

A vector of chi-squared random variates

quantile

Parameterized quantile function

text

Parameterized title of distribution

Details

Generates random variates from the chi-squared distribution.

Chi-Squared variates are generated by inverting uniform(0,1) variates produced either by stats::runif (if stream is NULL) or by rstream::rstream.sample (if stream is not NULL). In either case, stats::qchisq is used to invert the uniform(0,1) variate(s). In this way, using vchisq provides a monotone and synchronized binomial variate generator, although not particularly fast.

The stream indicated must be an integer between 1 and 25 inclusive.

The chi-squared distribution with df = $n\ge 0$ degrees of freedom has density

$$f_n(x)=\frac{1}{2^{n/2}\mathrm{\Gamma }(n/2)}{x}^{n/2-1}{e}^{-x/2}$$

for $x>0$. The mean and variance are $n$ and $2n$.

The non-central chi-squared distribution with df = n degrees of freedom and non-centrality parameter ncp $=\lambda$ has density

$$f(x)=e^{-\lambda /2}\sum _{r=0}^{\mathrm{\infty }}\frac{(\lambda /2{)}^r}{r!}{f}_{n+2r}(x)$$

for $x\ge 0$.

See Also

rstream, set.seed, stats::runif

stats::rchisq

Examples

# NOT RUN {
 set.seed(8675309)
 # NOTE: following inverts rstream::rstream.sample using stats::qchisq
 vchisq(3, df = 3, ncp = 2)

 set.seed(8675309)
 # NOTE: following inverts rstream::rstream.sample using stats::qchisq
 vchisq(3, 3, stream = 1)
 vchisq(3, 3, stream = 2)

 set.seed(8675309)
 # NOTE: following inverts rstream::rstream.sample using stats::qchisq
 vchisq(1, 3, stream = 1)
 vchisq(1, 3, stream = 2)
 vchisq(1, 3, stream = 1)
 vchisq(1, 3, stream = 2)
 vchisq(1, 3, stream = 1)
 vchisq(1, 3, stream = 2)

 set.seed(8675309)
 variates <- vchisq(1000, 3, stream = 1)
 set.seed(8675309)
 variates <- vchisq(1000, 3, stream = 1, antithetic = TRUE)

# }