Inequalities in Rényi’s theorem. (English. Russian original) Zbl 0834.60025

Kartashov, N. V.

Theory Probab. Math. Stat. 45, 23-28 (1992); translation from Teor. Veroyatn. Mat. Stat., Kiev 45, 27-33 (1991).

Summary: Some new inequalities are given for the deviation in the uniform metric of the distribution function of the sum of a random geometric number of independent identically distributed nonnegative random variables, from the corresponding exponential function. The right-hand sides of the estimates have first order of smallness with respect to the small parameter of a geometric distribution and contain also the second moment of the terms. The question of best possible constants is considered.

MSC:

60F05	Central limit and other weak theorems
41A25	Rate of convergence, degree of approximation
60G50	Sums of independent random variables; random walks
60K05	Renewal theory

Keywords:

inequalities; uniform metric; small parameter of a geometric distribution; best possible constants