S - Distributions : A Class of Continuous Heavy Tail Distributions To Model Erratic Data

S - Distributions : A Class of Continuous Heavy Tail Distributions To Model Erratic Data

Erratic data has recently become very frequent due to political. economical sharp turbulence and natural disasters. Classical distributions in statistics in general fail to model erratic data. We introduce new heavy tail Cauchy type distributions on O. Ox), called here S-distributions, that appear to be very power full tools and easily applicable in modeling erratic data. We apply S-distributions to variety sets of real data including. AMEX, FOREX, NASDAQ stocks price. Theoretical contributions include introducing new one-sided kernels that has link to the generalized Linnik distributions, new integral formulas including an extension for the Kotz-Ostrovski (1996) mixture representation. The existence of S-distributions appears to be a very challenging problem in mathematical statistics. We provide a constructive solution.