simEd (version 2.0.1)

vbinom: Variate Generation for Binomial Distribution

Description

Variate Generation for Binomial Distribution

Usage

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

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

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

Author

Barry Lawson (),
Larry Leemis (),
Vadim Kudlay ()

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 \(x = 0, \ldots, n\).

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)