Variate Generation for Chi-Squared Distribution
Variate Generation for Chi-Squared Distribution
vchisq(n, df, ncp = 0, stream = NULL, antithetic = FALSE, asList = FALSE)
n |
number of observations |
df |
Degrees of freedom (non-negative, but can be non-integer) |
ncp |
Non-centrality parameter (non-negative) |
stream |
if |
antithetic |
if |
asList |
if |
Generates random variates from the chi-squared distribution.
Chi-Squared 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::qchisq is used to
invert the uniform(0,1) variate(s).
In this way, using vchisq 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 chi-squared distribution with df = n >= 0 degrees
of freedom has density
f_n(x) = 1 / (2^(n/2) Γ(n/2)) x^(n/2-1) e^(-x/2)
for x > 0. The mean and variance are n and 2n.
The non-central chi-squared distribution with df = n degrees of
freedom and non-centrality parameter ncp = λ has density
f(x) = exp(-λ/2) SUM_{r=0}^∞ ((λ/2)^r / r!) dchisq(x, df + 2r)
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 chi-squared 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::qchisq vchisq(3, df = 3, ncp = 2) set.seed(8675309) # NOTE: following inverts rstream::rstream.sample using stats::qchisq vchisq(3, 3, stream = 1) vchisq(3, 3, stream = 2) set.seed(8675309) # NOTE: following inverts rstream::rstream.sample using stats::qchisq vchisq(1, 3, stream = 1) vchisq(1, 3, stream = 2) vchisq(1, 3, stream = 1) vchisq(1, 3, stream = 2) vchisq(1, 3, stream = 1) vchisq(1, 3, stream = 2) set.seed(8675309) variates <- vchisq(1000, 3, stream = 1) set.seed(8675309) variates <- vchisq(1000, 3, stream = 1, antithetic = TRUE)
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