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<html><head><title>R: Maximum-likelihood Fitting of Univariate Distributions</title>
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<table width="100%" summary="page for fitdistr {MASS}"><tr><td>fitdistr {MASS}</td><td align="right">R Documentation</td></tr></table>
<h2>Maximum-likelihood Fitting of Univariate Distributions</h2>
<h3>Description</h3>
<p>
Maximum-likelihood fitting of univariate distributions, allowing
parameters to be held fixed if desired.
</p>
<h3>Usage</h3>
<pre>
fitdistr(x, densfun, start, ...)
</pre>
<h3>Arguments</h3>
<table summary="R argblock">
<tr valign="top"><td><code>x</code></td>
<td>
A numeric vector.
</td></tr>
<tr valign="top"><td><code>densfun</code></td>
<td>
Either a character string or a function returning a density evaluated
at its first argument.
<br>
Distributions <code>"beta"</code>, <code>"cauchy"</code>, <code>"chi-squared"</code>,
<code>"exponential"</code>, <code>"f"</code>, <code>"gamma"</code>, <code>"geometric"</code>,
<code>"log-normal"</code>, <code>"lognormal"</code>, <code>"logistic"</code>,
<code>"negative binomial"</code>, <code>"normal"</code>, <code>"Poisson"</code>,
<code>"t"</code> and <code>"weibull"</code> are recognised, case being ignored.
</td></tr>
<tr valign="top"><td><code>start</code></td>
<td>
A named list giving the parameters to be optimized with initial
values. This can be omitted for some of the named distributions and
must be for others (see Details).
</td></tr>
<tr valign="top"><td><code>...</code></td>
<td>
Additional parameters, either for <code>densfun</code> or for <code>optim</code>.
In particular, it can be used to specify bounds via <code>lower</code> or
<code>upper</code> or both. If arguments of <code>densfun</code> (or the density
function corresponding to a character-string specification) are included
they will be held fixed.
</td></tr>
</table>
<h3>Details</h3>
<p>
For the Normal, log-Normal, exponential and Poisson distributions the
closed-form MLEs (and exact standard errors) are used, and
<code>start</code> should not be supplied.
</p>
<p>
For all other distributions, direct optimization of the log-likelihood
is performed using <code><a href="../../stats/html/optim.html">optim</a></code>. The estimated standard
errors are taken from the observed information matrix, calculated by a
numerical approximation. For one-dimensional problems the Nelder-Mead
method is used and for multi-dimensional problems the BFGS method,
unless arguments named <code>lower</code> or <code>upper</code> are supplied when
<code>L-BFGS-B</code> is used or <code>method</code> is supplied explicitly.
</p>
<p>
For the <code>"t"</code> named distribution the density is taken to be the
location-scale family with location <code>m</code> and scale <code>s</code>.
</p>
<p>
For the following named distributions, reasonable starting values will
be computed if <code>start</code> is omitted or only partially specified:
<code>"cauchy"</code>, <code>"gamma"</code>, <code>"logistic"</code>,
<code>"negative binomial"</code> (parametrized by <code>mu</code> and
<code>size</code>), <code>"t"</code> and <code>"weibull"</code>. Note that these
starting values may not be good enough if the fit is poor: in
particular they are not resistant to outliers unless the fitted
distribution is long-tailed.
</p>
<p>
There are <code><a href="../../stam/html/stam-internal.html">print</a></code>, <code><a href="../../vars/html/coefficients.html">coef</a></code> and
<code><a href="../../vars/html/logLik.html">logLik</a></code> methods for class <code>"fitdistr"</code>.
</p>
<h3>Value</h3>
<p>
An object of class <code>"fitdistr"</code>, a list with three components,
</p>
<table summary="R argblock">
<tr valign="top"><td><code>estimate</code></td>
<td>
the parameter estimates,</td></tr>
<tr valign="top"><td><code>sd</code></td>
<td>
the estimated standard errors, and</td></tr>
<tr valign="top"><td><code>loglik</code></td>
<td>
the log-likelihood.</td></tr>
</table>
<h3>References</h3>
<p>
Venables, W. N. and Ripley, B. D. (2002)
<EM>Modern Applied Statistics with S.</EM> Fourth edition. Springer.
</p>
<h3>Examples</h3>
<pre>
set.seed(123)
x <- rgamma(100, shape = 5, rate = 0.1)
fitdistr(x, "gamma")
## now do this directly with more control.
fitdistr(x, dgamma, list(shape = 1, rate = 0.1), lower = 0.01)
set.seed(123)
x2 <- rt(250, df = 9)
fitdistr(x2, "t", df = 9)
## allow df to vary: not a very good idea!
fitdistr(x2, "t")
## now do fixed-df fit directly with more control.
mydt <- function(x, m, s, df) dt((x-m)/s, df)/s
fitdistr(x2, mydt, list(m = 0, s = 1), df = 9, lower = c(-Inf, 0))
set.seed(123)
x3 <- rweibull(100, shape = 4, scale = 100)
fitdistr(x3, "weibull")
set.seed(123)
x4 <- rnegbin(500, mu = 5, theta = 4)
fitdistr(x4, "Negative Binomial") # R only
</pre>
<hr><div align="center">[Package <em>MASS</em> version 7.2-44 <a href="00Index.html">Index]</a></div>
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