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<section id="numpy-random-randomstate-binomial">
<h1>numpy.random.RandomState.binomial<a class="headerlink" href="#numpy-random-randomstate-binomial" title="Link to this heading">#</a></h1>
<p>method</p>
<dl class="py method">
<dt class="sig sig-object py" id="numpy.random.RandomState.binomial">
<span class="sig-prename descclassname"><span class="pre">random.RandomState.</span></span><span class="sig-name descname"><span class="pre">binomial</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">p</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.RandomState.binomial" title="Link to this definition">#</a></dt>
<dd><p>Draw samples from a binomial distribution.</p>
<p>Samples are drawn from a binomial distribution with specified
parameters, n trials and p probability of success where
n an integer >= 0 and p is in the interval [0,1]. (n may be
input as a float, but it is truncated to an integer in use)</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.binomial.html#numpy.random.Generator.binomial" title="numpy.random.Generator.binomial"><code class="xref py py-obj docutils literal notranslate"><span class="pre">binomial</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>n</strong><span class="classifier">int or array_like of ints</span></dt><dd><p>Parameter of the distribution, >= 0. Floats are also accepted,
but they will be truncated to integers.</p>
</dd>
<dt><strong>p</strong><span class="classifier">float or array_like of floats</span></dt><dd><p>Parameter of the distribution, >= 0 and <=1.</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">n</span></code> and <code class="docutils literal notranslate"><span class="pre">p</span></code> are both scalars.
Otherwise, <code class="docutils literal notranslate"><span class="pre">np.broadcast(n,</span> <span class="pre">p).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 binomial distribution, where
each sample is equal to the number of successes over the n trials.</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.binom.html#scipy.stats.binom" title="(in SciPy v1.15.2)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">scipy.stats.binom</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.binomial.html#numpy.random.Generator.binomial" title="numpy.random.Generator.binomial"><code class="xref py py-obj docutils literal notranslate"><span class="pre">random.Generator.binomial</span></code></a></dt><dd><p>which should be used for new code.</p>
</dd>
</dl>
</div>
<p class="rubric">Notes</p>
<p>The probability mass function (PMF) for the binomial distribution is</p>
<div class="math notranslate nohighlight">
\[P(N) = \binom{n}{N}p^N(1-p)^{n-N},\]</div>
<p>where <span class="math notranslate nohighlight">\(n\)</span> is the number of trials, <span class="math notranslate nohighlight">\(p\)</span> is the probability
of success, and <span class="math notranslate nohighlight">\(N\)</span> is the number of successes.</p>
<p>When estimating the standard error of a proportion in a population by
using a random sample, the normal distribution works well unless the
product p*n <=5, where p = population proportion estimate, and n =
number of samples, in which case the binomial distribution is used
instead. For example, a sample of 15 people shows 4 who are left
handed, and 11 who are right handed. Then p = 4/15 = 27%. 0.27*15 = 4,
so the binomial distribution should be used in this case.</p>
<p class="rubric">References</p>
<div role="list" class="citation-list">
<div class="citation" id="rba9e0e258624-1" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
<p>Dalgaard, Peter, “Introductory Statistics with R”,
Springer-Verlag, 2002.</p>
</div>
<div class="citation" id="rba9e0e258624-2" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></span>
<p>Glantz, Stanton A. “Primer of Biostatistics.”, McGraw-Hill,
Fifth Edition, 2002.</p>
</div>
<div class="citation" id="rba9e0e258624-3" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>3<span class="fn-bracket">]</span></span>
<p>Lentner, Marvin, “Elementary Applied Statistics”, Bogden
and Quigley, 1972.</p>
</div>
<div class="citation" id="rba9e0e258624-4" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>4<span class="fn-bracket">]</span></span>
<p>Weisstein, Eric W. “Binomial Distribution.” From MathWorld–A
Wolfram Web Resource.
<a class="reference external" href="https://mathworld.wolfram.com/BinomialDistribution.html">https://mathworld.wolfram.com/BinomialDistribution.html</a></p>
</div>
<div class="citation" id="rba9e0e258624-5" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>5<span class="fn-bracket">]</span></span>
<p>Wikipedia, “Binomial distribution”,
<a class="reference external" href="https://en.wikipedia.org/wiki/Binomial_distribution">https://en.wikipedia.org/wiki/Binomial_distribution</a></p>
</div>
</div>
<p class="rubric">Examples</p>
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<div class="try_examples_button_container"><button class="try_examples_button" onclick="window.tryExamplesShowIframe('e80de525-6cdd-4748-9ac4-b9ad5f412ed4','e65bb462-2143-40cc-8276-159e89c54430','4195c1a6-143b-4419-9156-9af70ecae907','../../../lite/tree/../notebooks/index.html?path=bee521f6_4f85_4b88_829e_d42fc52e62c1.ipynb','None')">Try it in your browser!</button></div><div class="try_examples_content docutils container">
<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">n</span><span class="p">,</span> <span class="n">p</span> <span class="o">=</span> <span class="mi">10</span><span class="p">,</span> <span class="mf">.5</span> <span class="c1"># number of trials, probability of each trial</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">binomial</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">p</span><span class="p">,</span> <span class="mi">1000</span><span class="p">)</span>
<span class="go"># result of flipping a coin 10 times, tested 1000 times.</span>
</pre></div>
</div>
<p>A real world example. A company drills 9 wild-cat oil exploration
wells, each with an estimated probability of success of 0.1. All nine
wells fail. What is the probability of that happening?</p>
<p>Let’s do 20,000 trials of the model, and count the number that
generate zero positive results.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="nb">sum</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">binomial</span><span class="p">(</span><span class="mi">9</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">,</span> <span class="mi">20000</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span><span class="p">)</span><span class="o">/</span><span class="mf">20000.</span>
<span class="go"># answer = 0.38885, or 38%.</span>
</pre></div>
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