update docs

Author: ZebinYang

docs/_build/html/_sources/guides/data/twosample_test.rst.txt

@@ -17,7 +17,7 @@ Distance Metrics
 
 .. math::
    \begin{align}     
-      PSI = \sum^{B}_{i=1} (p(x) - q(x))ln (\frac{p(x)}{q(x)}),
+      PSI = \sum^{B}_{i=1} (p(x_i) - q(x_i))ln \frac{p(x_i)}{q(x_i)},
    \end{align}
 
 where :math:`B` is the number of bins, :math:`p(x)` and :math:`q(x)` is the empirical density function of the base and target population, respectively. Note that the PSI calculation is related to the binning method, and we have two options for binning, i.e., "uniform" and "quantile". The number of bins is fixed at 10.
@@ -26,7 +26,7 @@ where :math:`B` is the number of bins, :math:`p(x)` and :math:`q(x)` is the empi
 
 .. math::
    \begin{align}
-      WD_{1} = \sum^{B}_{i=1} |P(x) - Q(x)|,
+      WD_{1} = \int |P(x) - Q(x)| dx,
    \end{align}
 
 where and :math:`P(x)` and :math:`Q(x)` are the cumulative distribution of the target and base population. 
@@ -35,11 +35,11 @@ where and :math:`P(x)` and :math:`Q(x)` are the cumulative distribution of the t
 
 .. math::
    \begin{align}     
-      KS = \max |P(x) - Q(x)|,
+      KS = \sup_x |P(x) - Q(x)|.
    \end{align}
 
-In PiML, the WD1 and KS statistics are calculated by the `wasserstein_distance` and `ks_2samp` functions from `scipy.stats`, where we don't need to specify the binning method. 
- 
+In PiML, the WD1 and KS statistics are calculated by the `wasserstein_distance` and `ks_2samp` functions from `scipy.stats`.
+
 
 Usage
 ^^^^^^^^^^^^^^^^^^^^^^^^^

docs/_build/html/guides/data/twosample_test.html

@@ -256,25 +256,25 @@ <h2><span class="section-number">2.7.1. </span>Distance Metrics<a class="headerl
 </ul>
 <div class="math notranslate nohighlight">
 \[\begin{align}
-   PSI = \sum^{B}_{i=1} (p(x) - q(x))ln (\frac{p(x)}{q(x)}),
+   PSI = \sum^{B}_{i=1} (p(x_i) - q(x_i))ln \frac{p(x_i)}{q(x_i)},
 \end{align}\]</div>
 <p>where <span class="math notranslate nohighlight">\(B\)</span> is the number of bins, <span class="math notranslate nohighlight">\(p(x)\)</span> and <span class="math notranslate nohighlight">\(q(x)\)</span> is the empirical density function of the base and target population, respectively. Note that the PSI calculation is related to the binning method, and we have two options for binning, i.e., “uniform” and “quantile”. The number of bins is fixed at 10.</p>
 <ul class="simple">
 <li><p><strong>Wasserstein distance 1D (WD1)</strong>: WD1 calculates the absolute difference between the cumulative distribution functions of the two samples.</p></li>
 </ul>
 <div class="math notranslate nohighlight">
 \[\begin{align}
-   WD_{1} = \sum^{B}_{i=1} |P(x) - Q(x)|,
+   WD_{1} = \int |P(x) - Q(x)| dx,
 \end{align}\]</div>
 <p>where and <span class="math notranslate nohighlight">\(P(x)\)</span> and <span class="math notranslate nohighlight">\(Q(x)\)</span> are the cumulative distribution of the target and base population.</p>
 <ul class="simple">
 <li><p><strong>Kolmogorov-Smirnov (KS)</strong>: KS calculates the maximum absolute distance between the cumulative distribution functions of the two samples. In PiML, the WD1 statistics are calculated by the function from <code class="docutils literal notranslate"><span class="pre">scipy.stats</span></code>.</p></li>
 </ul>
 <div class="math notranslate nohighlight">
 \[\begin{align}
-   KS = \max |P(x) - Q(x)|,
+   KS = \sup_x |P(x) - Q(x)|.
 \end{align}\]</div>
-<p>In PiML, the WD1 and KS statistics are calculated by the <code class="docutils literal notranslate"><span class="pre">wasserstein_distance</span></code> and <code class="docutils literal notranslate"><span class="pre">ks_2samp</span></code> functions from <code class="docutils literal notranslate"><span class="pre">scipy.stats</span></code>, where we don’t need to specify the binning method.</p>
+<p>In PiML, the WD1 and KS statistics are calculated by the <code class="docutils literal notranslate"><span class="pre">wasserstein_distance</span></code> and <code class="docutils literal notranslate"><span class="pre">ks_2samp</span></code> functions from <code class="docutils literal notranslate"><span class="pre">scipy.stats</span></code>.</p>
 </section>
 <section id="usage">
 <h2><span class="section-number">2.7.2. </span>Usage<a class="headerlink" href="#usage" title="Permalink to this heading">¶</a></h2>