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<section id="numpy-random-f">
<h1>numpy.random.f<a class="headerlink" href="#numpy-random-f" title="Link to this heading">#</a></h1>
<dl class="py function">
<dt class="sig sig-object py" id="numpy.random.f">
<span class="sig-prename descclassname"><span class="pre">random.</span></span><span class="sig-name descname"><span class="pre">f</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dfnum</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dfden</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">size</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#numpy.random.f" title="Link to this definition">#</a></dt>
<dd><p>Draw samples from an F distribution.</p>
<p>Samples are drawn from an F distribution with specified parameters,
<em class="xref py py-obj">dfnum</em> (degrees of freedom in numerator) and <em class="xref py py-obj">dfden</em> (degrees of
freedom in denominator), where both parameters must be greater than
zero.</p>
<p>The random variate of the F distribution (also known as the
Fisher distribution) is a continuous probability distribution
that arises in ANOVA tests, and is the ratio of two chi-square
variates.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>New code should use the <a class="reference internal" href="numpy.random.Generator.f.html#numpy.random.Generator.f" title="numpy.random.Generator.f"><code class="xref py py-obj docutils literal notranslate"><span class="pre">f</span></code></a>
method of a <a class="reference internal" href="../generator.html#numpy.random.Generator" title="numpy.random.Generator"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Generator</span></code></a> instance instead;
please see the <a class="reference internal" href="../index.html#random-quick-start"><span class="std std-ref">Quick start</span></a>.</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>dfnum</strong><span class="classifier">float or array_like of floats</span></dt><dd><p>Degrees of freedom in numerator, must be > 0.</p>
</dd>
<dt><strong>dfden</strong><span class="classifier">float or array_like of float</span></dt><dd><p>Degrees of freedom in denominator, must be > 0.</p>
</dd>
<dt><strong>size</strong><span class="classifier">int or tuple of ints, optional</span></dt><dd><p>Output shape. If the given shape is, e.g., <code class="docutils literal notranslate"><span class="pre">(m,</span> <span class="pre">n,</span> <span class="pre">k)</span></code>, then
<code class="docutils literal notranslate"><span class="pre">m</span> <span class="pre">*</span> <span class="pre">n</span> <span class="pre">*</span> <span class="pre">k</span></code> samples are drawn. If size is <code class="docutils literal notranslate"><span class="pre">None</span></code> (default),
a single value is returned if <code class="docutils literal notranslate"><span class="pre">dfnum</span></code> and <code class="docutils literal notranslate"><span class="pre">dfden</span></code> are both scalars.
Otherwise, <code class="docutils literal notranslate"><span class="pre">np.broadcast(dfnum,</span> <span class="pre">dfden).size</span></code> samples are drawn.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>out</strong><span class="classifier">ndarray or scalar</span></dt><dd><p>Drawn samples from the parameterized Fisher distribution.</p>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.f.html#scipy.stats.f" title="(in SciPy v1.15.2)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">scipy.stats.f</span></code></a></dt><dd><p>probability density function, distribution or cumulative density function, etc.</p>
</dd>
<dt><a class="reference internal" href="numpy.random.Generator.f.html#numpy.random.Generator.f" title="numpy.random.Generator.f"><code class="xref py py-obj docutils literal notranslate"><span class="pre">random.Generator.f</span></code></a></dt><dd><p>which should be used for new code.</p>
</dd>
</dl>
</div>
<p class="rubric">Notes</p>
<p>The F statistic is used to compare in-group variances to between-group
variances. Calculating the distribution depends on the sampling, and
so it is a function of the respective degrees of freedom in the
problem. The variable <em class="xref py py-obj">dfnum</em> is the number of samples minus one, the
between-groups degrees of freedom, while <em class="xref py py-obj">dfden</em> is the within-groups
degrees of freedom, the sum of the number of samples in each group
minus the number of groups.</p>
<p class="rubric">References</p>
<div role="list" class="citation-list">
<div class="citation" id="r068cb77115ef-1" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
<p>Glantz, Stanton A. “Primer of Biostatistics.”, McGraw-Hill,
Fifth Edition, 2002.</p>
</div>
<div class="citation" id="r068cb77115ef-2" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></span>
<p>Wikipedia, “F-distribution”,
<a class="reference external" href="https://en.wikipedia.org/wiki/F-distribution">https://en.wikipedia.org/wiki/F-distribution</a></p>
</div>
</div>
<p class="rubric">Examples</p>
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<p>An example from Glantz[1], pp 47-40:</p>
<p>Two groups, children of diabetics (25 people) and children from people
without diabetes (25 controls). Fasting blood glucose was measured,
case group had a mean value of 86.1, controls had a mean value of
82.2. Standard deviations were 2.09 and 2.49 respectively. Are these
data consistent with the null hypothesis that the parents diabetic
status does not affect their children’s blood glucose levels?
Calculating the F statistic from the data gives a value of 36.01.</p>
<p>Draw samples from the distribution:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">dfnum</span> <span class="o">=</span> <span class="mf">1.</span> <span class="c1"># between group degrees of freedom</span>
<span class="gp">>>> </span><span class="n">dfden</span> <span class="o">=</span> <span class="mf">48.</span> <span class="c1"># within groups degrees of freedom</span>
<span class="gp">>>> </span><span class="n">s</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">f</span><span class="p">(</span><span class="n">dfnum</span><span class="p">,</span> <span class="n">dfden</span><span class="p">,</span> <span class="mi">1000</span><span class="p">)</span>
</pre></div>
</div>
<p>The lower bound for the top 1% of the samples is :</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">sort</span><span class="p">(</span><span class="n">s</span><span class="p">)[</span><span class="o">-</span><span class="mi">10</span><span class="p">]</span>
<span class="go">7.61988120985 # random</span>
</pre></div>
</div>
<p>So there is about a 1% chance that the F statistic will exceed 7.62,
the measured value is 36, so the null hypothesis is rejected at the 1%
level.</p>
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