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<a href="Scientific-module.html">Package Scientific</a> ::
Package Statistics
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<!-- ==================== PACKAGE DESCRIPTION ==================== -->
<h1 class="epydoc">Package Statistics</h1><p class="nomargin-top"></p>
<p>Basic monovariate statistics</p>
<!-- ==================== SUBMODULES ==================== -->
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<span class="table-header">Submodules</span></td>
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<ul class="nomargin">
<li> <strong class="uidlink"><a href="Scientific.Statistics.Histogram-module.html">Scientific.Statistics.Histogram</a></strong>: <em class="summary">Standard and weighted histograms</em> </li>
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<!-- ==================== FUNCTIONS ==================== -->
<a name="section-Functions"></a>
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<span class="table-header">Functions</span></td>
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<span class="summary-type">number</span>
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<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Statistics-module.html#average" class="summary-sig-name">average</a>(<span class="summary-sig-arg">data</span>)</span><br />
Mean (average value, first moment)</td>
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</td>
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</table>
</td>
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<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type">number</span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Statistics-module.html#correlation" class="summary-sig-name">correlation</a>(<span class="summary-sig-arg">data1</span>,
<span class="summary-sig-arg">data2</span>)</span><br />
Calculates the correlation coefficient between two data sequences</td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type">number</span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Statistics-module.html#kurtosis" class="summary-sig-name">kurtosis</a>(<span class="summary-sig-arg">data</span>)</span><br />
Kurtosis (fourth normalized moment)</td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type">number</span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Statistics-module.html#mean" class="summary-sig-name">mean</a>(<span class="summary-sig-arg">data</span>)</span><br />
Mean (average value, first moment)</td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type">number</span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Statistics-module.html#median" class="summary-sig-name">median</a>(<span class="summary-sig-arg">data</span>)</span><br />
Median</td>
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</td>
</tr>
</table>
</td>
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<span class="summary-type"> </span>
</td><td class="summary">
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<tr>
<td><span class="summary-sig"><a name="mode"></a><span class="summary-sig-name">mode</span>(<span class="summary-sig-arg">data</span>)</span></td>
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</td>
</tr>
</table>
</td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type">number</span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Statistics-module.html#moment" class="summary-sig-name">moment</a>(<span class="summary-sig-arg">data</span>,
<span class="summary-sig-arg">order</span>,
<span class="summary-sig-arg">about</span>=<span class="summary-sig-default">None</span>,
<span class="summary-sig-arg">theoretical</span>=<span class="summary-sig-default">1</span>)</span><br />
Calculate the moments of the distribution corresponding to a set of
data</td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type">number</span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Statistics-module.html#normalizedMoment" class="summary-sig-name">normalizedMoment</a>(<span class="summary-sig-arg">data</span>,
<span class="summary-sig-arg">order</span>)</span><br />
Calculate the normalized moments of the distribution corresponding to
a set of data.</td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type">number</span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Statistics-module.html#skewness" class="summary-sig-name">skewness</a>(<span class="summary-sig-arg">data</span>)</span><br />
Skewness (third normalized moment)</td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type">number</span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Statistics-module.html#standardDeviation" class="summary-sig-name">standardDeviation</a>(<span class="summary-sig-arg">data</span>)</span><br />
Standard deviation</td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type">number</span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Statistics-module.html#variance" class="summary-sig-name">variance</a>(<span class="summary-sig-arg">data</span>)</span><br />
Variance (second moment)</td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type"><code>tuple</code> of two elements</span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Statistics-module.html#weightedMean" class="summary-sig-name">weightedMean</a>(<span class="summary-sig-arg">data</span>,
<span class="summary-sig-arg">sigma</span>)</span><br />
Weighted mean of a sequence of numbers with given standard deviations</td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
</table>
<!-- ==================== FUNCTION DETAILS ==================== -->
<a name="section-FunctionDetails"></a>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr bgcolor="#70b0f0" class="table-header">
<td align="left" colspan="2" class="table-header">
<span class="table-header">Function Details</span></td>
</tr>
</table>
<a name="average"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">average</span>(<span class="sig-arg">data</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<p>Mean (average value, first moment)</p>
<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>data</code></strong> (<code>list</code> or <code>Numeric.array</code>) - a sequence of numbers</li>
</ul></dd>
<dt>Returns: number</dt>
<dd>the mean of the number sequence</dd>
</dl>
</td></tr></table>
</div>
<a name="correlation"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">correlation</span>(<span class="sig-arg">data1</span>,
<span class="sig-arg">data2</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<p>Calculates the correlation coefficient between two data sequences</p>
<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>data1</code></strong> (<code>Numeric.array</code> or <code>list</code>) - first data sequence</li>
<li><strong class="pname"><code>data2</code></strong> (<code>Numeric.array</code> or <code>list</code>) - second data sequence of length identical to data1</li>
</ul></dd>
<dt>Returns: number</dt>
<dd>the correlation coefficient between data1 and data2</dd>
<dt>Raises:</dt>
<dd><ul class="nomargin-top">
<li><code><strong class='fraise'>ValueError</strong></code> - if data1 and data2 have different lengths</li>
</ul></dd>
</dl>
</td></tr></table>
</div>
<a name="kurtosis"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">kurtosis</span>(<span class="sig-arg">data</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<p>Kurtosis (fourth normalized moment)</p>
<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>data</code></strong> (<code>list</code> or <code>Numeric.array</code>) - a sequence of numbers</li>
</ul></dd>
<dt>Returns: number</dt>
<dd>the kurtosis of the number sequence</dd>
</dl>
</td></tr></table>
</div>
<a name="mean"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">mean</span>(<span class="sig-arg">data</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<p>Mean (average value, first moment)</p>
<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>data</code></strong> (<code>list</code> or <code>Numeric.array</code>) - a sequence of numbers</li>
</ul></dd>
<dt>Returns: number</dt>
<dd>the mean of the number sequence</dd>
</dl>
</td></tr></table>
</div>
<a name="median"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">median</span>(<span class="sig-arg">data</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<p>Median</p>
<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>data</code></strong> (<code>list</code> or <code>Numeric.array</code>) - a sequence of numbers</li>
</ul></dd>
<dt>Returns: number</dt>
<dd>the median of the number sequence</dd>
</dl>
</td></tr></table>
</div>
<a name="moment"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">moment</span>(<span class="sig-arg">data</span>,
<span class="sig-arg">order</span>,
<span class="sig-arg">about</span>=<span class="sig-default">None</span>,
<span class="sig-arg">theoretical</span>=<span class="sig-default">1</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<p>Calculate the moments of the distribution corresponding to a set of
data</p>
<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>data</code></strong> (<code>Numeric.array</code> of numbers) - a sequence of data points</li>
<li><strong class="pname"><code>order</code></strong> (<code>int</code>) - the order of the moment to be calculated</li>
<li><strong class="pname"><code>about</code></strong> (number) - the center of the distribution. If <code>None</code>, use the
mean value as the center.</li>
<li><strong class="pname"><code>theoretical</code></strong> - for internal use</li>
</ul></dd>
<dt>Returns: number</dt>
<dd>the moment of the given order about the specified center</dd>
</dl>
</td></tr></table>
</div>
<a name="normalizedMoment"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">normalizedMoment</span>(<span class="sig-arg">data</span>,
<span class="sig-arg">order</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<p>Calculate the normalized moments of the distribution corresponding to
a set of data. Normalization means division by the n-th power of the
standard deviation.</p>
<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>data</code></strong> (<code>Numeric.array</code> of numbers) - a sequence of data points</li>
<li><strong class="pname"><code>order</code></strong> (<code>int</code>) - the order of the moment to be calculated</li>
</ul></dd>
<dt>Returns: number</dt>
<dd>the normalized moment of the given order</dd>
</dl>
</td></tr></table>
</div>
<a name="skewness"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">skewness</span>(<span class="sig-arg">data</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<p>Skewness (third normalized moment)</p>
<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>data</code></strong> (<code>list</code> or <code>Numeric.array</code>) - a sequence of numbers</li>
</ul></dd>
<dt>Returns: number</dt>
<dd>the skewness of the number sequence</dd>
</dl>
</td></tr></table>
</div>
<a name="standardDeviation"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">standardDeviation</span>(<span class="sig-arg">data</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<p>Standard deviation</p>
<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>data</code></strong> (<code>list</code> or <code>Numeric.array</code>) - a sequence of numbers</li>
</ul></dd>
<dt>Returns: number</dt>
<dd>the standard deviation of the number sequence</dd>
</dl>
</td></tr></table>
</div>
<a name="variance"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">variance</span>(<span class="sig-arg">data</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<p>Variance (second moment)</p>
<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>data</code></strong> (<code>list</code> or <code>Numeric.array</code>) - a sequence of numbers</li>
</ul></dd>
<dt>Returns: number</dt>
<dd>the variance of the number sequence</dd>
</dl>
</td></tr></table>
</div>
<a name="weightedMean"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">weightedMean</span>(<span class="sig-arg">data</span>,
<span class="sig-arg">sigma</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<p>Weighted mean of a sequence of numbers with given standard
deviations</p>
<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>data</code></strong> (<code>list</code> or <code>Numeric.array</code>) - a sequence of measurements</li>
<li><strong class="pname"><code>sigma</code></strong> (<code>list</code> or <code>Numeric.array</code>) - a sequence of corresponding standard deviations</li>
</ul></dd>
<dt>Returns: <code>tuple</code> of two elements</dt>
<dd>the weighted mean and corresponding standard deviation</dd>
</dl>
</td></tr></table>
</div>
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