simEd (version 2.0.0)

vbeta: Variate Generation for Beta Distribution

Description

Variate Generation for Beta Distribution

Usage

vbeta(
  n,
  shape1,
  shape2,
  ncp = 0,
  stream = NULL,
  antithetic = FALSE,
  asList = FALSE
)

Arguments

n

number of observations

shape1

Shape parameter 1 (alpha)

shape2

Shape parameter 2 (beta)

ncp

Non-centrality parameter (default 0)

stream

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

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 beta random variates

quantile

Parameterized quantile function

text

Parameterized title of distribution

Details

Generates random variates from the beta distribution.

Beta 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::qbeta is used to invert the uniform(0,1) variate(s). In this way, using vbeta 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 beta distribution has density

$$f(x) = \frac{\Gamma(a+b)}{\Gamma(a) \ \Gamma(b)} x^{a-1}(1-x)^{b-1}$$

for \(a > 0\), \(b > 0\) and \(0 \leq x \leq 1\) where the boundary values at \(x=0\) or \(x=1\) are defined as by continuity (as limits).

The mean is \(\frac{a}{a+b}\) and the variance is \({ab}{(a+b)^2 (a+b+1)}\)

See Also

rstream, set.seed, stats::runif

stats::rbeta

Examples

# NOT RUN {
 set.seed(8675309)
 # NOTE: following inverts rstream::rstream.sample using stats::qbeta
 vbeta(3, shape1 = 3, shape2 = 1, ncp = 2)

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

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

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

# }