vbinom: Variate Generation for Binomial Distribution

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Variate Generation for Binomial Distribution

Description

Variate Generation for Binomial Distribution

Usage

vbinom(n, size, prob, stream = NULL, antithetic = FALSE, asList = FALSE)

Arguments

n	number of observations
size	number of trials (zero or more)
prob	probability of success on each trial (0 < prob \le 1)
stream	if NULL (default), uses stats::runif to generate uniform variates to invert via stats::qbinom; otherwise, an integer in 1:25 indicates the rstream stream from which to generate uniform variates to invert via stats::qbinom;
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 binomial distribution.

Binomial 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::qbinom is used to invert the uniform(0,1) variate(s). In this way, using vbinom 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 binomial distribution with parameters size = n and prob = p has pmf

p(x) = {n \choose x} p^x (1-p)^{(n-x)}

for x = 0, \ldots, n.

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 binomial 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::rbinom

Examples

 set.seed(8675309)
 # NOTE: following inverts rstream::rstream.sample using stats::qbinom
 vbinom(3, size = 10, prob = 0.25)

 set.seed(8675309)
 # NOTE: following inverts rstream::rstream.sample using stats::qbinom
 vbinom(3, 10, 0.25, stream = 1)
 vbinom(3, 10, 0.25, stream = 2)

 set.seed(8675309)
 # NOTE: following inverts rstream::rstream.sample using stats::qbinom
 vbinom(1, 10, 0.25, stream = 1)
 vbinom(1, 10, 0.25, stream = 2)
 vbinom(1, 10, 0.25, stream = 1)
 vbinom(1, 10, 0.25, stream = 2)
 vbinom(1, 10, 0.25, stream = 1)
 vbinom(1, 10, 0.25, stream = 2)

 set.seed(8675309)
 variates <- vbinom(100, 10, 0.25, stream = 1)
 set.seed(8675309)
 variates <- vbinom(100, 10, 0.25, stream = 1, antithetic = TRUE)

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