simEd (version 2.0.0)

vfd: 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::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 FALSE random variates

quantile

Parameterized quantile function

text

Parameterized title of distribution

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::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 \(x > 0\).

See Also

rstream, set.seed, stats::runif

stats::rf

Examples

# NOT RUN {
 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(1000, 5, 5, stream = 1)
 set.seed(8675309)
 variates <- vfd(1000, 5, 5, stream = 1, antithetic = TRUE)

# }