We use numerical maximum likelihood estimation to obtain the parameters governing probability distributions that might plausibly generate the daily, weekly, monthly, or quarterly return distributions of stocks from the Dow 30. The candidate distribution types should probably be continuous and supported on the whole real line. So, we choose to investigate the Gaussian distribution, Student's -distribution, the Gumbel distribution, the Cauchy distribution, and the Laplace distribution. We show a histogram of the return data for a particular time horizon and frequency, as well as the density function with the fitted parameters.
Explore the various possible distribution choices to see which one(s) fit the empirical returns. Some choices for some return frequencies are clearly better than other choices!