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<h3 class="section">26.2 Basic Statistical Functions</h3>
<p>Octave supports various helpful statistical functions. Many are useful as
initial steps to prepare a data set for further analysis. Others provide
different measures from those of the basic descriptive statistics.
<!-- center scripts/statistics/base/center.m -->
<p><a name="doc_002dcenter"></a>
<div class="defun">
— Function File: <b>center</b> (<var>x</var>)<var><a name="index-center-2445"></a></var><br>
— Function File: <b>center</b> (<var>x, dim</var>)<var><a name="index-center-2446"></a></var><br>
<blockquote><p>If <var>x</var> is a vector, subtract its mean.
If <var>x</var> is a matrix, do the above for each column.
If the optional argument <var>dim</var> is given, operate along this dimension.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dzscore.html#doc_002dzscore">zscore</a>.
</p></blockquote></div>
<!-- zscore scripts/statistics/base/zscore.m -->
<p><a name="doc_002dzscore"></a>
<div class="defun">
— Function File: <b>zscore</b> (<var>x</var>)<var><a name="index-zscore-2447"></a></var><br>
— Function File: <b>zscore</b> (<var>x, dim</var>)<var><a name="index-zscore-2448"></a></var><br>
<blockquote><p>If <var>x</var> is a vector, subtract its mean and divide by its standard
deviation.
<p>If <var>x</var> is a matrix, do the above along the first non-singleton
dimension.
If the optional argument <var>dim</var> is given, operate along this dimension.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dcenter.html#doc_002dcenter">center</a>.
</p></blockquote></div>
<!-- histc scripts/statistics/base/histc.m -->
<p><a name="doc_002dhistc"></a>
<div class="defun">
— Function File: <var>n</var> = <b>histc</b> (<var>x, edges</var>)<var><a name="index-histc-2449"></a></var><br>
— Function File: <var>n</var> = <b>histc</b> (<var>x, edges, dim</var>)<var><a name="index-histc-2450"></a></var><br>
— Function File: [<var>n</var>, <var>idx</var>] = <b>histc</b> (<var><small class="dots">...</small></var>)<var><a name="index-histc-2451"></a></var><br>
<blockquote><p>Produce histogram counts.
<p>When <var>x</var> is a vector, the function counts the number of elements of
<var>x</var> that fall in the histogram bins defined by <var>edges</var>. This must be
a vector of monotonically increasing values that define the edges of the
histogram bins. <var>n</var><code>(k)</code> contains the number of elements in
<var>x</var> for which <var>edges</var><code>(k) <= </code><var>x</var><code> < </code><var>edges</var><code>(k+1)</code>.
The final element of <var>n</var> contains the number of elements of <var>x</var>
exactly equal to the last element of <var>edges</var>.
<p>When <var>x</var> is an N-dimensional array, the computation is
carried out along dimension <var>dim</var>. If not specified <var>dim</var> defaults
to the first non-singleton dimension.
<p>When a second output argument is requested an index matrix is also returned.
The <var>idx</var> matrix has the same size as <var>x</var>. Each element of <var>idx</var>
contains the index of the histogram bin in which the corresponding element
of <var>x</var> was counted.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dhist.html#doc_002dhist">hist</a>.
</p></blockquote></div>
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<!-- nchoosek scripts/specfun/nchoosek.m -->
<p><a name="doc_002dnchoosek"></a>
<div class="defun">
— Function File: <var>c</var> = <b>nchoosek</b> (<var>n, k</var>)<var><a name="index-nchoosek-2452"></a></var><br>
— Function File: <var>c</var> = <b>nchoosek</b> (<var>set, k</var>)<var><a name="index-nchoosek-2453"></a></var><br>
<blockquote>
<p>Compute the binomial coefficient or all combinations of a set of items.
<p>If <var>n</var> is a scalar then calculate the binomial coefficient
of <var>n</var> and <var>k</var> which is defined as
<pre class="example"> / \
| n | n (n-1) (n-2) ... (n-k+1) n!
| | = ------------------------- = ---------
| k | k! k! (n-k)!
\ /
</pre>
<p class="noindent">This is the number of combinations of <var>n</var> items taken in groups of
size <var>k</var>.
<p>If the first argument is a vector, <var>set</var>, then generate all
combinations of the elements of <var>set</var>, taken <var>k</var> at a time, with
one row per combination. The result <var>c</var> has <var>k</var> columns and
<code>nchoosek (length (</code><var>set</var><code>), </code><var>k</var><code>)</code><!-- /@w --> rows.
<p>For example:
<p>How many ways can three items be grouped into pairs?
<pre class="example"> nchoosek (3, 2)
⇒ 3
</pre>
<p>What are the possible pairs?
<pre class="example"> nchoosek (1:3, 2)
⇒ 1 2
1 3
2 3
</pre>
<p><code>nchoosek</code> works only for non-negative, integer arguments. Use
<code>bincoeff</code> for non-integer and negative scalar arguments, or for
computing many binomial coefficients at once with vector inputs
for <var>n</var> or <var>k</var>.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dbincoeff.html#doc_002dbincoeff">bincoeff</a>, <a href="doc_002dperms.html#doc_002dperms">perms</a>.
</p></blockquote></div>
<!-- perms scripts/specfun/perms.m -->
<p><a name="doc_002dperms"></a>
<div class="defun">
— Function File: <b>perms</b> (<var>v</var>)<var><a name="index-perms-2454"></a></var><br>
<blockquote>
<p>Generate all permutations of <var>v</var>, one row per permutation. The
result has size <code>factorial (</code><var>n</var><code>) * </code><var>n</var>, where <var>n</var>
is the length of <var>v</var>.
<p>As an example, <code>perms([1, 2, 3])</code> returns the matrix
<pre class="example"> 1 2 3
2 1 3
1 3 2
2 3 1
3 1 2
3 2 1
</pre>
</blockquote></div>
<!-- ranks scripts/statistics/base/ranks.m -->
<p><a name="doc_002dranks"></a>
<div class="defun">
— Function File: <b>ranks</b> (<var>x, dim</var>)<var><a name="index-ranks-2455"></a></var><br>
<blockquote><p>Return the ranks of <var>x</var> along the first non-singleton dimension
adjusted for ties. If the optional argument <var>dim</var> is
given, operate along this dimension.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dspearman.html#doc_002dspearman">spearman</a>, <a href="doc_002dkendall.html#doc_002dkendall">kendall</a>.
</p></blockquote></div>
<!-- run_count scripts/statistics/base/run_count.m -->
<p><a name="doc_002drun_005fcount"></a>
<div class="defun">
— Function File: <b>run_count</b> (<var>x, n</var>)<var><a name="index-run_005fcount-2456"></a></var><br>
— Function File: <b>run_count</b> (<var>x, n, dim</var>)<var><a name="index-run_005fcount-2457"></a></var><br>
<blockquote><p>Count the upward runs along the first non-singleton dimension of
<var>x</var> of length 1, 2, <small class="dots">...</small>, <var>n</var>-1 and greater than or equal
to <var>n</var>.
<p>If the optional argument <var>dim</var> is given then operate
along this dimension.
</p></blockquote></div>
<!-- runlength scripts/statistics/base/runlength.m -->
<p><a name="doc_002drunlength"></a>
<div class="defun">
— Function File: [count, value] = <b>runlength</b> (<var>x</var>)<var><a name="index-runlength-2458"></a></var><br>
<blockquote><p>Find the lengths of all sequences of common values. Return the
vector of lengths and the value that was repeated.
<pre class="example"> runlength ([2, 2, 0, 4, 4, 4, 0, 1, 1, 1, 1])
⇒ [2, 1, 3, 1, 4]
</pre>
</blockquote></div>
<!-- probit scripts/statistics/base/probit.m -->
<p><a name="doc_002dprobit"></a>
<div class="defun">
— Function File: <b>probit</b> (<var>p</var>)<var><a name="index-probit-2459"></a></var><br>
<blockquote><p>For each component of <var>p</var>, return the probit (the quantile of the
standard normal distribution) of <var>p</var>.
</p></blockquote></div>
<!-- logit scripts/statistics/base/logit.m -->
<p><a name="doc_002dlogit"></a>
<div class="defun">
— Function File: <b>logit</b> (<var>p</var>)<var><a name="index-logit-2460"></a></var><br>
<blockquote><p>For each component of <var>p</var>, return the logit of <var>p</var> defined as
<pre class="example"> logit (<var>p</var>) = log (<var>p</var> / (1-<var>p</var>))
</pre>
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dlogistic_005fcdf.html#doc_002dlogistic_005fcdf">logistic_cdf</a>.
</p></blockquote></div>
<!-- cloglog scripts/statistics/base/cloglog.m -->
<p><a name="doc_002dcloglog"></a>
<div class="defun">
— Function File: <b>cloglog</b> (<var>x</var>)<var><a name="index-cloglog-2461"></a></var><br>
<blockquote><p>Return the complementary log-log function of <var>x</var>, defined as
<pre class="example"> cloglog (x) = - log (- log (<var>x</var>))
</pre>
</blockquote></div>
<!-- mahalanobis scripts/statistics/base/mahalanobis.m -->
<p><a name="doc_002dmahalanobis"></a>
<div class="defun">
— Function File: <b>mahalanobis</b> (<var>x, y</var>)<var><a name="index-mahalanobis-2462"></a></var><br>
<blockquote><p>Return the Mahalanobis' D-square distance between the multivariate
samples <var>x</var> and <var>y</var>, which must have the same number of
components (columns), but may have a different number of observations
(rows).
</p></blockquote></div>
<!-- table scripts/statistics/base/table.m -->
<p><a name="doc_002dtable"></a>
<div class="defun">
— Function File: [<var>t</var>, <var>l_x</var>] = <b>table</b> (<var>x</var>)<var><a name="index-table-2463"></a></var><br>
— Function File: [<var>t</var>, <var>l_x</var>, <var>l_y</var>] = <b>table</b> (<var>x, y</var>)<var><a name="index-table-2464"></a></var><br>
<blockquote><p>Create a contingency table <var>t</var> from data vectors. The <var>l_x</var> and
<var>l_y</var> vectors are the corresponding levels.
<p>Currently, only 1- and 2-dimensional tables are supported.
</p></blockquote></div>
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