title: Averaging normalized pd.crosstab values across different dataframes
body: <p>I have a large number of dataframes, say 50 in the format</p>
  <div class="s-table-container">
  <table class="s-table">
  <thead>
  <tr>
  <th>Date</th>
  <th>Observations</th>
  </tr>
  </thead>
  <tbody>
  <tr>
  <td>18.02.2020</td>
  <td>29</td>
  </tr>
  <tr>
  <td>19.02.2020</td>
  <td>42</td>
  </tr>
  </tbody>
  </table>
  </div>
  <p>And I have a common dataframe also in the same format:</p>
  <div class="s-table-container">
  <table class="s-table">
  <thead>
  <tr>
  <th>Date</th>
  <th>Observations_common</th>
  </tr>
  </thead>
  <tbody>
  <tr>
  <td>15.02.2020</td>
  <td>30</td>
  </tr>
  <tr>
  <td>16.02.2020</td>
  <td>34</td>
  </tr>
  <tr>
  <td>18.02.2020</td>
  <td>42</td>
  </tr>
  <tr>
  <td>19.02.2020</td>
  <td>39</td>
  </tr>
  </tbody>
  </table>
  </div>
  <p>I merged each of these dataframes with the common one on date such that I have a dataframe in the format:</p>
  <div class="s-table-container">
  <table class="s-table">
  <thead>
  <tr>
  <th>Date</th>
  <th>Observations_common</th>
  <th>Observations</th>
  </tr>
  </thead>
  <tbody>
  <tr>
  <td>18.02.2020</td>
  <td>42</td>
  <td>29</td>
  </tr>
  <tr>
  <td>19.02.2020</td>
  <td>39</td>
  <td>42</td>
  </tr>
  </tbody>
  </table>
  </div>
  <p>Now I did pd.crosstab between &quot;Observations_common&quot; and &quot;Observations&quot; to obtain a relation based on counts and a normalized heatmap (that means the aggregation function is now a pdf in the heatmap from 0-1)</p>
  <p><a href="https://i.stack.imgur.com/88bdD.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/88bdD.jpg" alt="enter image description here" /></a></p>
  <p>Now I want to construct a composite series by averaging
  all the PDFs of all the available observations for every day, so
  instead of one count for each day, I get a distribution based on all available Observations.</p>
  <p>Is there any way to extract the pdfs for each day from a crosstab or heatmap for all the dataframes?
  I am trying to replicate the method described in page 5 of this article: <a href="https://www.aanda.org/articles/aa/pdf/2017/06/aa30045-16.pdf" rel="nofollow noreferrer">https://www.aanda.org/articles/aa/pdf/2017/06/aa30045-16.pdf</a></p>