Probability and moment bounds for sums of negatively associated random variables. (English. Ukrainian original) Zbl 0923.60024

Matula, Przemysław

Theory Probab. Math. Stat. 55, 135-141 (1997); translation from Teor. Jmovirn. Mat. Stat. 55, 130-135 (1996).

Let \(S_n=\sum_{i=1}^n x_i\), where \(x_i\), \(i\geq 1\), are negatively associated (NA) random variables. A number of Fuk-Nagaev type upper bounds for tail probabilities \(P(S_n\geq x)\) and moments \(E| S_n| ^p\) are obtained. For instance, if \(Ex_k=0\), \(E| x_k| ^p<\infty \) for all \(k\geq 1\) and some \(p>2\), then \(| S_n| ^p\leq c(\sum_{i=1}^n E| x_i| ^p+(\sum_{i=1}^n Ex_i^2)^{p/2}))\). Such inequalities are used to investigate the asymptotic behaviour of empirical distribution functions based on a sequence of identically distributed NA random variables.

Reviewer: N.M.Zinchenko (Kyïv)

MSC:

60E15	Inequalities; stochastic orderings
60F10	Large deviations

Keywords:

negative association; covariance; tail probability; moment bound; empirical distribution function