vfd: Variate Generation for FALSE Distribution

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Variate Generation for FALSE Distribution

Description

Variate Generation for FALSE Distribution

Usage

vfd(n, df1, df2, ncp = 0, stream = NULL, antithetic = FALSE, asList = FALSE)

Arguments

n	number of observations
df1	Degrees of freedom > 0
df2	Degrees of freedom > 0
ncp	Non-centrality parameter >= 0
stream	if NULL (default), uses stats::runif to generate uniform variates to invert via stats::qf; otherwise, an integer in 1:25 indicates the rstream stream from which to generate uniform variates to invert via stats::qf;
antithetic	if FALSE (default), inverts u = uniform(0,1) variate(s) generated via either stats::runif or 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 FALSE distribution.

FALSE variates are generated by inverting uniform(0,1) variates produced either by stats::runif (if stream is NULL) or by rstream.sample (if stream is not NULL). In either case, stats::qf is used to invert the uniform(0,1) variate(s). In this way, using vfd 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 F distribution with df1 = n_1 and df2 = n_2 degrees of freedom has density

f(x) = \frac {\Gamma(n_1/2 + n_2/2)} {\Gamma(n_1/2) \ \Gamma(n_2/2)} \left( \frac{n_1}{n_2} \right)^{n_1/2} x^{n_1/2 - 1} \left( 1 + \frac{n_1x}{n_2} \right) ^ {-(n_1 + n_2)/2}

for x > 0.

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 FALSE 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::rf

Examples

 set.seed(8675309)
 # NOTE: following inverts rstream::rstream.sample using stats::qf
 vfd(3, df1 = 1, df2 = 2, ncp = 10)

 set.seed(8675309)
 # NOTE: following inverts rstream::rstream.sample using stats::qf
 vfd(3, 5, 5, stream = 1)
 vfd(3, 5, 5, stream = 2)

 set.seed(8675309)
 # NOTE: following inverts rstream::rstream.sample using stats::qf
 vfd(1, 5, 5, stream = 1)
 vfd(1, 5, 5, stream = 2)
 vfd(1, 5, 5, stream = 1)
 vfd(1, 5, 5, stream = 2)
 vfd(1, 5, 5, stream = 1)
 vfd(1, 5, 5, stream = 2)

 set.seed(8675309)
 variates <- vfd(100, 5, 5, stream = 1)
 set.seed(8675309)
 variates <- vfd(100, 5, 5, stream = 1, antithetic = TRUE)

simEd documentation built on Sept. 9, 2025, 5:58 p.m.