title: Fitting a Poisson distribution to data in statsmodels
body: <p>I am trying to fit a Poisson distribution to my data using statsmodels but I am confused by the results that I am getting and how to use the library.</p>
  
  <p>My real data will be a series of numbers that I think that I should be able to describe as having a poisson distribution plus some outliers so eventually I would like to do a robust fit to the data.</p>
  
  <p>However for testing purposes, I just create a dataset using scipy.stats.poisson</p>
  
  <pre><code>samp = scipy.stats.poisson.rvs(4,size=200)
  </code></pre>
  
  <p>So to fit this using statsmodels I think that I just need to have a constant 'endog'</p>
  
  <pre><code>res = sm.Poisson(samp,np.ones_like(samp)).fit()
  </code></pre>
  
  <p>print res.summary()</p>
  
  <pre><code>                          Poisson Regression Results
  ==============================================================================
  Dep. Variable:                      y   No. Observations:                  200
  Model:                        Poisson   Df Residuals:                      199
  Method:                           MLE   Df Model:                            0
  Date:                Fri, 27 Jun 2014   Pseudo R-squ.:                   0.000
  Time:                        14:28:29   Log-Likelihood:                -404.37
  converged:                       True   LL-Null:                       -404.37
                                          LLR p-value:                       nan
  ==============================================================================
                   coef    std err          z      P&gt;|z|      [95.0% Conf. Int.]
  ------------------------------------------------------------------------------
  const          1.3938      0.035     39.569      0.000         1.325     1.463
  ==============================================================================
  </code></pre>
  
  <p>Ok, that doesn't look right, But if I do</p>
  
  <pre><code>res.predict()
  </code></pre>
  
  <p>I get an array of 4.03 (which was the mean for this test sample).
  So basically, firstly I very confused how to interpret this result from statsmodel and secondly I should probably being doing something completely different if I'm interested in robust parameter estimation of a distribution rather than fitting trends but how should I go about doing that?</p>
  
  <p><strong>Edit</strong>
  I should really have given more detail in order to answer the second part of my question. </p>
  
  <p>I have an event that occurs a random time after a starting time. When I plot a histogram of the delay times for many events, I see that the distribution looks like a scaled Poisson distribution plus several outlier points which are normally caused by issues in my underlying system. So I simply wanted to find the expected time delay for the dataset, excluding the outliers. If not for the outliers, I could simply find the mean time. I suppose that I could exclude them manually but I thought that I could find something more exacting. </p>
  
  <p><strong>Edit</strong>
  On further reflection, I will be considering other distributions instead of sticking with a Poissonion and the details of my issue are probably a distraction from the original question but I've left them here anyway.</p>