simEd (version 2.0.0)

vpois: 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

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

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 \(E(X) = Var(X) = \lambda\)

See Also

rstream, set.seed, stats::runif

stats::rpois

Examples

# NOT RUN {
 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(1000, 3, stream = 1)
 set.seed(8675309)
 variates <- vpois(1000, 3, stream = 1, antithetic = TRUE)

# }