vbeta: Variate Generation for Beta Distribution

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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

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

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

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

Author(s)

Barry Lawson ([e-mail]),
Larry Leemis ([e-mail]),
Vadim Kudlay ([e-mail])

See Also

rstream, set.seed, stats::runif

stats::rbeta

Examples

 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(100, 3, 1, stream = 1)
 set.seed(8675309)
 variates <- vbeta(100, 3, 1, stream = 1, antithetic = TRUE)

simEd documentation built on Nov. 27, 2023, 1:07 a.m.