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