Atsitiktinių dydžių sumos serijų schemoje tankio funkcijos asimptotinis skleidinys didžiųjų nuokrypių Kramerio zonoje

Abstract

In this work, the expansion of the density function of series schemes of independent variables ksi^(n)_1, ksi^(n)_2, ... , ksi^(n)_j, with means Eksi^(n)_j = 0, and dispersions {sigma^(n)_j}^2 = Eksi^{(n)^2}_j has been obtained in the Cramer zone of large deviations. The result was obtained, based on General Lemma 6.1 [2] by joining the methods of characteristic functions and cumulants. The work broadens theory of sums of random variables [1] and in special case improves S.A. Book [5] results of sums of random variables with weights.