ON THE CONSTRUCTION OF MULTIMODAL MULTIPARAMETER EXPONENTIAL FAMILIES PROBABILITY LAWS

V.O. Rvachov, T.V. Rvachova

A new method of approximate computation of the normalizing factor of multiparameter multimodal exponential density families is proposed with the help of the generalized Taylor series for infinitely differentiable functions based on atomic functions which are the special solutions with a compact support of ordinary linear functional differential equations with constant coefficients and linear deviations of argument which possess good approximation properties.

Key words: multimodal multiparameter exponential density families, atomic function, the generalized Taylor series, basic functions of the generalized Taylor series.