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<title>GNU Scientific Library &ndash; Reference Manual: Resampling from histograms</title>

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<a name="Resampling-from-histograms"></a>
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<p>
Next: <a href="The-histogram-probability-distribution-struct.html#The-histogram-probability-distribution-struct" accesskey="n" rel="next">The histogram probability distribution struct</a>, Previous: <a href="Reading-and-writing-histograms.html#Reading-and-writing-histograms" accesskey="p" rel="previous">Reading and writing histograms</a>, Up: <a href="Histograms.html#Histograms" accesskey="u" rel="up">Histograms</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<hr>
<a name="Resampling-from-histograms-1"></a>
<h3 class="section">23.9 Resampling from histograms</h3>
<a name="index-resampling-from-histograms"></a>
<a name="index-sampling-from-histograms"></a>
<a name="index-probability-distributions_002c-from-histograms"></a>

<p>A histogram made by counting events can be regarded as a measurement of
a probability distribution.  Allowing for statistical error, the height
of each bin represents the probability of an event where the value of
<em>x</em> falls in the range of that bin.  The probability distribution
function has the one-dimensional form <em>p(x)dx</em> where,
</p>
<div class="example">
<pre class="example">p(x) = n_i/ (N w_i)
</pre></div>

<p>In this equation <em>n_i</em> is the number of events in the bin which
contains <em>x</em>, <em>w_i</em> is the width of the bin and <em>N</em> is
the total number of events.  The distribution of events within each bin
is assumed to be uniform.
</p>



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