Kernel Density Estimation
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1 2 3 4 5 | <span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span><span class="kn">from</span> <span class="nn">scipy</span> <span class="kn">import</span> <span class="n">stats</span><span class="kn">import</span> <span class="nn">statsmodels.api</span> <span class="kn">as</span> <span class="nn">sm</span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span><span class="kn">from</span> <span class="nn">statsmodels.distributions.mixture_rvs</span> <span class="kn">import</span> <span class="n">mixture_rvs</span> |
A univariate example.
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1 | <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">12345</span><span class="p">)</span> |
In [3]:
1 2 | <span class="n">obs_dist1</span> <span class="o">=</span> <span class="n">mixture_rvs</span><span class="p">([</span><span class="o">.</span><span class="mi">25</span><span class="p">,</span><span class="o">.</span><span class="mi">75</span><span class="p">],</span> <span class="n">size</span><span class="o">=</span><span class="mi">10000</span><span class="p">,</span> <span class="n">dist</span><span class="o">=</span><span class="p">[</span><span class="n">stats</span><span class="o">.</span><span class="n">norm</span><span class="p">,</span> <span class="n">stats</span><span class="o">.</span><span class="n">norm</span><span class="p">],</span> <span class="n">kwargs</span> <span class="o">=</span> <span class="p">(</span><span class="nb">dict</span><span class="p">(</span><span class="n">loc</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span><span class="n">scale</span><span class="o">=.</span><span class="mi">5</span><span class="p">),</span><span class="nb">dict</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span><span class="n">scale</span><span class="o">=.</span><span class="mi">5</span><span class="p">)))</span> |
In [4]:
1 2 | <span class="n">kde</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">nonparametric</span><span class="o">.</span><span class="n">KDEUnivariate</span><span class="p">(</span><span class="n">obs_dist1</span><span class="p">)</span><span class="n">kde</span><span class="o">.</span><span class="n">fit</span><span class="p">()</span> |
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1 2 3 4 | <span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">8</span><span class="p">))</span><span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span><span class="n">ax</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">obs_dist1</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">normed</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">'red'</span><span class="p">)</span><span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">kde</span><span class="o">.</span><span class="n">support</span><span class="p">,</span> <span class="n">kde</span><span class="o">.</span><span class="n">density</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">'black'</span><span class="p">);</span> |
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1 2 3 4 5 | <span class="n">obs_dist2</span> <span class="o">=</span> <span class="n">mixture_rvs</span><span class="p">([</span><span class="o">.</span><span class="mi">25</span><span class="p">,</span><span class="o">.</span><span class="mi">75</span><span class="p">],</span> <span class="n">size</span><span class="o">=</span><span class="mi">10000</span><span class="p">,</span> <span class="n">dist</span><span class="o">=</span><span class="p">[</span><span class="n">stats</span><span class="o">.</span><span class="n">norm</span><span class="p">,</span> <span class="n">stats</span><span class="o">.</span><span class="n">beta</span><span class="p">],</span> <span class="n">kwargs</span> <span class="o">=</span> <span class="p">(</span><span class="nb">dict</span><span class="p">(</span><span class="n">loc</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span><span class="n">scale</span><span class="o">=.</span><span class="mi">5</span><span class="p">),</span><span class="nb">dict</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span><span class="n">scale</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span><span class="n">args</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="o">.</span><span class="mi">5</span><span class="p">))))</span><span class="n">kde2</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">nonparametric</span><span class="o">.</span><span class="n">KDEUnivariate</span><span class="p">(</span><span class="n">obs_dist2</span><span class="p">)</span><span class="n">kde2</span><span class="o">.</span><span class="n">fit</span><span class="p">()</span> |
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1 2 3 4 | <span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">8</span><span class="p">))</span><span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span><span class="n">ax</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">obs_dist2</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">normed</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">'red'</span><span class="p">)</span><span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">kde2</span><span class="o">.</span><span class="n">support</span><span class="p">,</span> <span class="n">kde2</span><span class="o">.</span><span class="n">density</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">'black'</span><span class="p">);</span> |
The fitted KDE object is a full non-parametric distribution.
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1 2 3 4 | <span class="n">obs_dist3</span> <span class="o">=</span> <span class="n">mixture_rvs</span><span class="p">([</span><span class="o">.</span><span class="mi">25</span><span class="p">,</span><span class="o">.</span><span class="mi">75</span><span class="p">],</span> <span class="n">size</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span> <span class="n">dist</span><span class="o">=</span><span class="p">[</span><span class="n">stats</span><span class="o">.</span><span class="n">norm</span><span class="p">,</span> <span class="n">stats</span><span class="o">.</span><span class="n">norm</span><span class="p">],</span> <span class="n">kwargs</span> <span class="o">=</span> <span class="p">(</span><span class="nb">dict</span><span class="p">(</span><span class="n">loc</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span><span class="n">scale</span><span class="o">=.</span><span class="mi">5</span><span class="p">),</span><span class="nb">dict</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span><span class="n">scale</span><span class="o">=.</span><span class="mi">5</span><span class="p">)))</span><span class="n">kde3</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">nonparametric</span><span class="o">.</span><span class="n">KDEUnivariate</span><span class="p">(</span><span class="n">obs_dist3</span><span class="p">)</span><span class="n">kde3</span><span class="o">.</span><span class="n">fit</span><span class="p">()</span> |
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1 | <span class="n">kde3</span><span class="o">.</span><span class="n">entropy</span> |
Out[9]:
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1 | <span class="n">kde3</span><span class="o">.</span><span class="n">evaluate</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span> |
Out[10]:
CDF
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1 2 3 | <span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">8</span><span class="p">))</span><span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span><span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">kde3</span><span class="o">.</span><span class="n">support</span><span class="p">,</span> <span class="n">kde3</span><span class="o">.</span><span class="n">cdf</span><span class="p">);</span> |
Cumulative Hazard Function
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1 2 3 | <span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">8</span><span class="p">))</span><span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span><span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">kde3</span><span class="o">.</span><span class="n">support</span><span class="p">,</span> <span class="n">kde3</span><span class="o">.</span><span class="n">cumhazard</span><span class="p">);</span> |
Inverse CDF
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1 2 3 | <span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">8</span><span class="p">))</span><span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span><span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">kde3</span><span class="o">.</span><span class="n">support</span><span class="p">,</span> <span class="n">kde3</span><span class="o">.</span><span class="n">icdf</span><span class="p">);</span> |
Survival Function
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1 2 3 | <span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">12</span><span class="p">,</span><span class="mi">8</span><span class="p">))</span><span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span><span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">kde3</span><span class="o">.</span><span class="n">support</span><span class="p">,</span> <span class="n">kde3</span><span class="o">.</span><span class="n">sf</span><span class="p">);</span> |
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