vpois: Variate Generation for Poisson Distribution

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Variate Generation for Poisson Distribution

Description

Variate Generation for Poisson Distribution

Usage

vpois(n, lambda, stream = NULL, antithetic = FALSE, asList = FALSE)

Arguments

n	number of observations
lambda	Rate of distribution
stream	if NULL (default), uses stats::runif to generate uniform variates to invert via stats::qpois; otherwise, an integer in 1:25 indicates the rstream stream from which to generate uniform variates to invert via stats::qpois;
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 Poisson distribution.

Poisson 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::qpois is used to invert the uniform(0,1) variate(s). In this way, using vpois 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 Poisson distribution has density

p(x) = \frac{\lambda^x e^{-\lambda}}{x!}

for x = 0, 1, 2, \ldots. The mean and variance are E(X) = Var(X) = \lambda

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 Poisson 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::rpois

Examples

 set.seed(8675309)
 # NOTE: following inverts rstream::rstream.sample using stats::qpois
 vpois(3, lambda = 5)

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

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

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

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