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<a name="Statistical-Plots"></a>
<div class="header">
<p>
Next: <a href="Correlation-and-Regression-Analysis.html#Correlation-and-Regression-Analysis" accesskey="n" rel="next">Correlation and Regression Analysis</a>, Previous: <a href="Basic-Statistical-Functions.html#Basic-Statistical-Functions" accesskey="p" rel="prev">Basic Statistical Functions</a>, Up: <a href="Statistics.html#Statistics" accesskey="u" rel="up">Statistics</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Statistical-Plots-1"></a>
<h3 class="section">26.3 Statistical Plots</h3>


<p>Octave can create Quantile Plots (QQ-Plots), and Probability Plots
(PP-Plots).  These are simple graphical tests for determining if a
data set comes from a certain distribution.
</p>
<p>Note that Octave can also show histograms of data
using the <code>hist</code> function as described in
<a href="Two_002dDimensional-Plots.html#Two_002dDimensional-Plots">Two-Dimensional Plots</a>.
</p>
<a name="XREFqqplot"></a><dl>
<dt><a name="index-qqplot"></a>: <em>[<var>q</var>, <var>s</var>] =</em> <strong>qqplot</strong> <em>(<var>x</var>)</em></dt>
<dt><a name="index-qqplot-1"></a>: <em>[<var>q</var>, <var>s</var>] =</em> <strong>qqplot</strong> <em>(<var>x</var>, <var>y</var>)</em></dt>
<dt><a name="index-qqplot-2"></a>: <em>[<var>q</var>, <var>s</var>] =</em> <strong>qqplot</strong> <em>(<var>x</var>, <var>dist</var>)</em></dt>
<dt><a name="index-qqplot-3"></a>: <em>[<var>q</var>, <var>s</var>] =</em> <strong>qqplot</strong> <em>(<var>x</var>, <var>y</var>, <var>params</var>)</em></dt>
<dt><a name="index-qqplot-4"></a>: <em></em> <strong>qqplot</strong> <em>(&hellip;)</em></dt>
<dd><p>Perform a QQ-plot (quantile plot).
</p>
<p>If F is the CDF of the distribution <var>dist</var> with parameters
<var>params</var> and G its inverse, and <var>x</var> a sample vector of length
<var>n</var>, the QQ-plot graphs ordinate <var>s</var>(<var>i</var>) = <var>i</var>-th
largest element of x versus abscissa <var>q</var>(<var>i</var>f) = G((<var>i</var> -
0.5)/<var>n</var>).
</p>
<p>If the sample comes from F, except for a transformation of location
and scale, the pairs will approximately follow a straight line.
</p>
<p>If the second argument is a vector <var>y</var> the empirical CDF of <var>y</var>
is used as <var>dist</var>.
</p>
<p>The default for <var>dist</var> is the standard normal distribution.  The
optional argument <var>params</var> contains a list of parameters of
<var>dist</var>.  For example, for a quantile plot of the uniform
distribution on [2,4] and <var>x</var>, use
</p>
<div class="example">
<pre class="example">qqplot (x, &quot;unif&quot;, 2, 4)
</pre></div>

<p><var>dist</var> can be any string for which a function <var>distinv</var> or
<var>dist_inv</var> exists that calculates the inverse CDF of distribution
<var>dist</var>.
</p>
<p>If no output arguments are given, the data are plotted directly.
</p></dd></dl>


<a name="XREFppplot"></a><dl>
<dt><a name="index-ppplot"></a>: <em>[<var>p</var>, <var>y</var>] =</em> <strong>ppplot</strong> <em>(<var>x</var>, <var>dist</var>, <var>params</var>)</em></dt>
<dd><p>Perform a PP-plot (probability plot).
</p>
<p>If F is the CDF of the distribution <var>dist</var> with parameters
<var>params</var> and <var>x</var> a sample vector of length <var>n</var>, the PP-plot
graphs ordinate <var>y</var>(<var>i</var>) = F (<var>i</var>-th largest element of
<var>x</var>) versus abscissa <var>p</var>(<var>i</var>) = (<var>i</var> - 0.5)/<var>n</var>.  If
the sample comes from F, the pairs will approximately follow a straight
line.
</p>
<p>The default for <var>dist</var> is the standard normal distribution.
</p>
<p>The optional argument <var>params</var> contains a list of parameters of
<var>dist</var>.
</p>
<p>For example, for a probability plot of the uniform distribution on [2,4]
and <var>x</var>, use
</p>
<div class="example">
<pre class="example">ppplot (x, &quot;uniform&quot;, 2, 4)
</pre></div>

<p><var>dist</var> can be any string for which a function <var>dist_cdf</var> that
calculates the CDF of distribution <var>dist</var> exists.
</p>
<p>If no output is requested then the data are plotted immediately.
</p></dd></dl>


<hr>
<div class="header">
<p>
Next: <a href="Correlation-and-Regression-Analysis.html#Correlation-and-Regression-Analysis" accesskey="n" rel="next">Correlation and Regression Analysis</a>, Previous: <a href="Basic-Statistical-Functions.html#Basic-Statistical-Functions" accesskey="p" rel="prev">Basic Statistical Functions</a>, Up: <a href="Statistics.html#Statistics" accesskey="u" rel="up">Statistics</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
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