Stable and generalized-t distributions and applications

In this paper a generalized-t distribution is introduced and used as an alternative to the symmetric stable distribution. To do so, the χ 2 -divergence is presented and minimized to approximate the symmetric stable distribution, as accurately as possible, by the generalized-t distribution. Kth moments for the generalized-t distribution function are given. The stable distribution is defined in terms of generalized hypergeometric functions. Five applications with natural data (sunspots activity), and financial data (stock exchange in Brazil, South Africa and Venezuela, and daily variation of Petrobras stock market) are analyzed. A time series analysis is used to eliminate data correlation in each data set, and then the distributions are used to fit the residuals of these models.