Variate Generation for FALSE Distribution
Variate Generation for FALSE Distribution
vfd(n, df1, df2, ncp = 0, stream = NULL, antithetic = FALSE, asList = FALSE)
n |
number of observations |
df1 |
Degrees of freedom > 0 |
df2 |
Degrees of freedom > 0 |
ncp |
Non-centrality parameter >= 0 |
stream |
if |
antithetic |
if |
asList |
if |
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 = n1 and df2
= n2 degrees of freedom has density
f(x) = Gamma((n1 + n2)/2) / (Gamma(n1/2) Gamma(n2/2)) (n1/n2)^(n1/2) x^(n1/2 - 1) (1 + (n1/n2) x)^-(n1 + n2)/2
for x > 0.
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 |
Barry Lawson (blawson@richmond.edu),
Larry Leemis (leemis@math.wm.edu),
Vadim Kudlay (vadim.kudlay@richmond.edu)
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)
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