title: GLM gamma regression in Python statsmodels
body: <p>Consider the GLM gamma function fitting in Python package statsmodel. </p>
  
  <p>Here is the code:</p>
  
  <pre><code>import numpy
  import statsmodels.api as sm
  
  model = sm.GLM(ytrain, xtrain, family=sm.families.Gamma(link = sm.genmod.families.links.identity)).fit()
  
  print model.summary()
  </code></pre>
  
  <p>This gives me the summary of the fitted model parameters, obtained by a gamma regression. What I am interested in, is the exact pdf $P(y | X)$ from the above model. What I can gather so far is the model.params*x gives the mean of the gamma as a function of the training data. How to infer the shape of the pdf from the summary ? </p>