title: How to find the best fitting parametric distribution for an empirical dataset (stock returns)?
body: <p>Given some real-valued empirical data (time series), I could convert it to a histogram to have an (non-parametric) <strong>empirical distribution</strong> of the data, but <strong>histograms</strong> are blocky and jagged.</p>
  <p>Instead, I would like to identify the best-fitting <strong>parametric distribution</strong> from the <code>scipy</code> or <code>scipy.stats</code> libraries of distribution functions, so that I can artificially generate a parametric distribution that closely fits the empirical distribution of my real data.</p>
  <p>If the empirical data are monthly returns of empirical AAPL stock returns, for example, I know that the parametric <strong>Johnson-SU distribution</strong> resembles, and can mimic, stock return distributions because of its customizable skew. However, the Johnson SU distribution in <code>scipy</code> requires four input parameters to be calibrated. How can I search for the best parameter settings of this parametric distribution from <code>scipy</code> that fits to the empirical distribution of my sample of AAPL returns?</p>