vgamma: Variate Generation for Gamma Distribution

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Variate Generation for Gamma Distribution

Description

Variate Generation for Gamma Distribution

Usage

vgamma(
  n,
  shape,
  rate = 1,
  scale = 1/rate,
  stream = NULL,
  antithetic = FALSE,
  asList = FALSE
)

Arguments

n	number of observations
shape	Shape parameter
rate	Alternate parameterization for scale
scale	Scale parameter
stream	if NULL (default), uses stats::runif to generate uniform variates to invert via stats::qgamma; otherwise, an integer in 1:25 indicates the rstream stream from which to generate uniform variates to invert via stats::qgamma;
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 gamma distribution.

Gamma 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::qgamma is used to invert the uniform(0,1) variate(s). In this way, using vgamma 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 gamma distribution with parameters \code{shape} = \eqn{a} and
\code{scale} = \eqn{s} has density

     \deqn{f(x) = \frac{1}{s^a\, \Gamma(a)} x^{a-1} e^{-x/s}}{
               f(x) = 1/(s^a Gamma(a)) x^(a-1) e^(-x/s)}

for \eqn{x \ge 0}, \eqn{a > 0}, and \eqn{s > 0}.
(Here \eqn{\Gamma(a)}{Gamma(a)} is the function implemented by
R's \code{\link[base:Special]{gamma}()} and defined in its help.)

The population mean and variance are \eqn{E(X) = as}
and \eqn{Var(X) = as^2}.

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 gamma 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::rgamma

Examples

 set.seed(8675309)
 # NOTE: following inverts rstream::rstream.sample using stats::qgamma
 vgamma(3, shape = 2, rate = 1)

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

 set.seed(8675309)
 # NOTE: following inverts rstream::rstream.sample using stats::qgamma
 vgamma(1, 2, scale = 1, stream = 1)
 vgamma(1, 2, scale = 1, stream = 2)
 vgamma(1, 2, scale = 1, stream = 1)
 vgamma(1, 2, scale = 1, stream = 2)
 vgamma(1, 2, scale = 1, stream = 1)
 vgamma(1, 2, scale = 1, stream = 2)

 set.seed(8675309)
 variates <- vgamma(100, 2, scale = 1, stream = 1)
 set.seed(8675309)
 variates <- vgamma(100, 2, scale = 1, stream = 1, antithetic = TRUE)

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