A tail bound for sums of independent random variables and application to the Pareto distribution.(English)Zbl 1195.60029

Let $$X_{i}, 1\leq i \leq n$$, be independent random variables with $$EX_{i}=0$$ and $$E|X_{i}|^{p}<\infty$$ for some $$p\geq 2$$. By making use of the Rosenthal inequality and the Bernstein inequality, the author derives an upper bound for the tail probability $$P(X_1 +\dots +X_{n}\geq t), t>0$$. This is first specialized to the case $$X_{i}=a_{i}Y_{i}$$, where $$a_{i}\in R$$ and $$Y_{i}, 1\leq i\leq n$$, have a common Pareto distribution. Then it is compared with the celebrated Fuk-Nagaev inequality.

MSC:

 6e+16 Inequalities; stochastic orderings
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