Classification rules for stable distributions

Often one is interested in identifying whether the financial market for a commodity has entered a “bullish” or a “bearish” characteristic. Stable or, more commonly, α-stable distributions, have been enhanced as a popular model for stock prices, and such change in characteristics may be related to the parameter(s) of these underlying distributions. This paper deals with discrimination between two stable distributions, or in turn, with classification of a new observation into one of two stable distributions. In case the parameters are unknown, we need training samples, one each from the two populations, which are utilized to provide necessary estimates. When the two index parameters, αs, can be held to be identical, but may be still unknown, we propose a quantile-based classification rule by exploiting a convolution type property and some results on the tail behavior of stable distributions. Fisher type rules are described for the general case. Details of the computer programs with necessary source codes are provided to enable the user to implement our rules for real-life data sets. An example based on a real-life data set provided to us by Rachev is also given.