Variate Generation for Cauchy Distribution
Variate Generation for Cauchy Distribution
vcauchy( n, location = 0, scale = 1, stream = NULL, antithetic = FALSE, asList = FALSE )
n |
number of observations |
location |
Location parameter (default 0) |
scale |
Scale parameter (default 1) |
stream |
if |
antithetic |
if |
asList |
if |
Generates random variates from the Cauchy distribution.
Cauchy 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::qcauchy is used to
invert the uniform(0,1) variate(s).
In this way, using vcauchy 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 Cauchy distribution has density
f(x) = f(x) = 1 / (π s (1 + ((x-l)/s)^2))
for all x.
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 Cauchy 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::qcauchy vcauchy(3, location = 3, scale = 1) set.seed(8675309) # NOTE: following inverts rstream::rstream.sample using stats::qcauchy vcauchy(3, 0, 3, stream = 1) vcauchy(3, 0, 3, stream = 2) set.seed(8675309) # NOTE: following inverts rstream::rstream.sample using stats::qcauchy vcauchy(1, 0, 3, stream = 1) vcauchy(1, 0, 3, stream = 2) vcauchy(1, 0, 3, stream = 1) vcauchy(1, 0, 3, stream = 2) vcauchy(1, 0, 3, stream = 1) vcauchy(1, 0, 3, stream = 2) set.seed(8675309) variates <- vcauchy(1000, 0, 3, stream = 1) set.seed(8675309) variates <- vcauchy(1000, 0, 3, stream = 1, antithetic = TRUE)
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