A Comparison of the GB2 and Skewed Generalized Log-t Distributions with an Application in Finance

Several families of statistical distributions have been used to model financial data. The four-parameter generalized beta of the second kind (GB2) and five-parameter skewed generalized t (SGT) have been fit to return and log-return data, respectively. We introduce the skewed generalized log-t (SGLT) distribution and note that the GB2 and SGLT share such distributions as the asymmetric log-Laplace (ALL), log-Laplace (LL), and log-normal (LN). We then compare the relative performance of the GB2 and SGLT in modeling the distribution of daily, weekly, and monthly stock return data. We find that the GB2 and SGLT perform similarly and that the three-parameter log-t (LT) distribution is quite robust.

Keywords: beta prime, double-Pareto, Feller-Pareto, SGT, stock returns