vnorm: Variate Generation for Normal Distribution

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Variate Generation for Normal Distribution

Description

Variate Generation for Normal Distribution

Usage

vnorm(n, mean = 0, sd = 1, stream = NULL, antithetic = FALSE, asList = FALSE)

Arguments

n	number of observations
mean	Mean of distribution (default 0)
sd	Standard deviation of distribution (default 1)
stream	if NULL (default), uses stats::runif to generate uniform variates to invert via stats::qnorm; otherwise, an integer in 1:25 indicates the rstream stream from which to generate uniform variates to invert via stats::qnorm;
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 normal distribution.

Normal 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::qnorm is used to invert the uniform(0,1) variate(s). In this way, using vnorm 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 normal distribution has density

 \deqn{f(x) = \frac{1}{\sqrt{2\pi}\sigma} e^{-(x - \mu)^2/(2 \sigma^2)}}{
           f(x) = 1/(\sqrt(2\pi)\sigma) e^(-(x - \mu)^2/(2 \sigma^2))}

for -\infty < x < \infty and \sigma > 0, where \mu is the mean of the distribution and \sigma the standard deviation.

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 normal 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::rnorm

Examples

 set.seed(8675309)
 # NOTE: following inverts rstream::rstream.sample using stats::qnorm
 vnorm(3, mean = 2, sd = 1)

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

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

 set.seed(8675309)
 variates <- vnorm(100, 10, 2, stream = 1)
 set.seed(8675309)
 variates <- vnorm(100, 10, 2, stream = 1, antithetic = TRUE)

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