ON THE CONSTRUCTION OF MULTIMODAL MULTIPARAMETER
EXPONENTIAL FAMILIES PROBABILITY LAWS

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.