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<html><head><title>R: Simulate from a Multivariate Normal Distribution</title>
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<table width="100%" summary="page for mvrnorm {MASS}"><tr><td>mvrnorm {MASS}</td><td align="right">R Documentation</td></tr></table>
<h2>Simulate from a Multivariate Normal Distribution</h2>
<h3>Description</h3>
<p>
Produces one or more samples from the specified
multivariate normal distribution.
</p>
<h3>Usage</h3>
<pre>
mvrnorm(n = 1, mu, Sigma, tol = 1e-6, empirical = FALSE)
</pre>
<h3>Arguments</h3>
<table summary="R argblock">
<tr valign="top"><td><code>n</code></td>
<td>
the number of samples required.
</td></tr>
<tr valign="top"><td><code>mu</code></td>
<td>
a vector giving the means of the variables.
</td></tr>
<tr valign="top"><td><code>Sigma</code></td>
<td>
a positive-definite symmetric matrix specifying the covariance matrix
of the variables.
</td></tr>
<tr valign="top"><td><code>tol</code></td>
<td>
tolerance (relative to largest variance) for numerical lack of
positive-definiteness in <code>Sigma</code>.
</td></tr>
<tr valign="top"><td><code>empirical</code></td>
<td>
logical. If true, mu and Sigma specify the empirical not population
mean and covariance matrix.
</td></tr>
</table>
<h3>Details</h3>
<p>
The matrix decomposition is done via <code>eigen</code>; although a Choleski
decomposition might be faster, the eigendecomposition is
stabler.
</p>
<h3>Value</h3>
<p>
If <code>n = 1</code> a vector of the same length as <code>mu</code>, otherwise an
<code>n</code> by <code>length(mu)</code> matrix with one sample in each row.</p>
<h3>Side Effects</h3>
<p>
Causes creation of the dataset <code>.Random.seed</code> if it does
not already exist, otherwise its value is updated.
</p>
<h3>References</h3>
<p>
B. D. Ripley (1987)
<EM>Stochastic Simulation.</EM>
Wiley. Page 98.
</p>
<h3>See Also</h3>
<p>
<code><a href="../../stats/html/Normal.html">rnorm</a></code>
</p>
<h3>Examples</h3>
<pre>
Sigma <- matrix(c(10,3,3,2),2,2)
Sigma
var(mvrnorm(n=1000, rep(0, 2), Sigma))
var(mvrnorm(n=1000, rep(0, 2), Sigma, empirical = TRUE))
</pre>
<hr><div align="center">[Package <em>MASS</em> version 7.2-44 <a href="00Index.html">Index]</a></div>
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