Variate Generation for Beta Distribution
Variate Generation for Beta Distribution
vbeta( n, shape1, shape2, ncp = 0, stream = NULL, antithetic = FALSE, asList = FALSE )
n |
number of observations |
shape1 |
Shape parameter 1 (alpha) |
shape2 |
Shape parameter 2 (beta) |
ncp |
Non-centrality parameter (default 0) |
stream |
if |
antithetic |
if |
asList |
if |
Generates random variates from the beta distribution.
Beta 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::qbeta is used to
invert the uniform(0,1) variate(s).
In this way, using vbeta 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 beta distribution has density
f(x) = Gamma(a+b)/(Gamma(a)Gamma(b)) x^(a-1)(1-x)^(b-1)
for a > 0, b > 0 and 0 <= x <= 1 where the boundary values at x=0 or x=1 are defined as by continuity (as limits).
The mean is a/(a+b) and the variance is ab/((a+b)^2 (a+b+1))
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 beta 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::qbeta vbeta(3, shape1 = 3, shape2 = 1, ncp = 2) set.seed(8675309) # NOTE: following inverts rstream::rstream.sample using stats::qbeta vbeta(3, 3, 1, stream = 1) vbeta(3, 3, 1, stream = 2) set.seed(8675309) # NOTE: following inverts rstream::rstream.sample using stats::qbeta vbeta(1, 3, 1, stream = 1) vbeta(1, 3, 1, stream = 2) vbeta(1, 3, 1, stream = 1) vbeta(1, 3, 1, stream = 2) vbeta(1, 3, 1, stream = 1) vbeta(1, 3, 1, stream = 2) set.seed(8675309) variates <- vbeta(1000, 3, 1, stream = 1) set.seed(8675309) variates <- vbeta(1000, 3, 1, stream = 1, antithetic = TRUE)
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