nicolasfauchereau/gist:294ba4273624b64a7315

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<h1 id="Illustration-of-PaCal-(Arithmetic-with-random-variables)">Illustration of <a href="http://pacal.sourceforge.net/">PaCal</a> (Arithmetic with random variables)<a class="anchor-link" href="#Illustration-of-PaCal-(Arithmetic-with-random-variables)">&#182;</a></h1>
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<div class=" highlight hl-ipython2"><pre><span class="o">%</span><span class="k">matplotlib</span> inline
<span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">pyplot</span> <span class="k">as</span> <span class="n">plt</span>
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<div class=" highlight hl-ipython2"><pre><span class="kn">from</span> <span class="nn">pacal</span> <span class="kn">import</span> <span class="o">*</span>
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<pre>Using compiled interpolation routine
Using compiled sparse grid routine
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<div class=" highlight hl-ipython2"><pre><span class="n">NormalDistr</span><span class="o">?</span>
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<div class=" highlight hl-ipython2"><pre><span class="n">X</span> <span class="o">=</span> <span class="n">NormalDistr</span><span class="p">(</span><span class="n">sym</span><span class="o">=</span><span class="s">&#39;X&#39;</span><span class="p">)</span>
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<div class=" highlight hl-ipython2"><pre><span class="n">Y</span> <span class="o">=</span> <span class="n">NormalDistr</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span> <span class="n">sym</span><span class="o">=</span><span class="s">&#39;Y&#39;</span><span class="p">)</span>
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<pre>#22190_4434034128+#22190_4402720528</pre>
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<div class=" highlight hl-ipython2"><pre><span class="n">S</span><span class="o">.</span><span class="n">summary</span><span class="p">()</span>
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<pre>============= summary =============
  N(0.0,1.0)+N(0,2)
                mean  =  8.3266726846886741e-16
                 var  =  5.0000000000000036
            skewness  =  -4.7664655742347595e-16
            kurtosis  =  2.9999999999999996
             entropy  =  2.2236574894217238
              median  =  -1.3322676295501878e-15
                mode  =  1.0674499837498935e-08
            medianad  =  1.5082049315656938
      iqrange(0.025)  =  8.765225405765802
      interval(0.95)  =  (-4.382612702882908, 4.382612702882893)
               range  =  (-inf, inf)
             tailexp  =  (-216.5841427655505, -216.5841427655505)
             int_err  =  -4.4408920985006262e-16
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<div class=" highlight hl-ipython2"><pre><span class="n">S</span><span class="o">.</span><span class="n">plot</span><span class="p">()</span>
<span class="n">Y</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">color</span><span class="o">=</span><span class="s">&#39;b&#39;</span><span class="p">)</span>
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<div class=" highlight hl-ipython2"><pre><span class="n">S</span><span class="o">.</span><span class="n">boxplot</span><span class="p">()</span>
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"
>
</div>

</div>

</div>
</div>

</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[11]:</div>
<div class="inner_cell">
    <div class="input_area">
<div class=" highlight hl-ipython2"><pre><span class="n">S</span><span class="o">.</span><span class="n">cdf</span><span class="p">(</span><span class="o">-</span><span class="mi">5</span><span class="p">)</span>
</pre></div>

</div>
</div>
</div>

<div class="output_wrapper">
<div class="output">


<div class="output_area"><div class="prompt output_prompt">Out[11]:</div>


<div class="output_text output_subarea output_execute_result">
<pre>0.012673659338734152</pre>
</div>

</div>

</div>
</div>

</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[12]:</div>
<div class="inner_cell">
    <div class="input_area">
<div class=" highlight hl-ipython2"><pre><span class="n">S</span><span class="o">.</span><span class="n">cdf</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
</pre></div>

</div>
</div>
</div>

<div class="output_wrapper">
<div class="output">


<div class="output_area"><div class="prompt output_prompt">Out[12]:</div>


<div class="output_text output_subarea output_execute_result">
<pre>0.98732634066126623</pre>
</div>

</div>

</div>
</div>

</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[13]:</div>
<div class="inner_cell">
    <div class="input_area">
<div class=" highlight hl-ipython2"><pre><span class="n">S</span><span class="o">.</span><span class="n">ccdf_value</span><span class="p">(</span><span class="mf">0.5</span><span class="p">)</span>
</pre></div>

</div>
</div>
</div>

<div class="output_wrapper">
<div class="output">


<div class="output_area"><div class="prompt output_prompt">Out[13]:</div>


<div class="output_text output_subarea output_execute_result">
<pre>0.41153163687906058</pre>
</div>

</div>

</div>
</div>

</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[14]:</div>
<div class="inner_cell">
    <div class="input_area">
<div class=" highlight hl-ipython2"><pre><span class="n">a</span> <span class="o">=</span> <span class="n">S</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">10000</span><span class="p">)</span>
</pre></div>

</div>
</div>
</div>

</div>
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="prompt input_prompt">In&nbsp;[16]:</div>
<div class="inner_cell">
    <div class="input_area">
<div class=" highlight hl-ipython2"><pre><span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="mi">20</span><span class="p">);</span>
</pre></div>

</div>
</div>
</div>

<div class="output_wrapper">
<div class="output">


<div class="output_area"><div class="prompt"></div>


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