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

Chesneau, Christophe

Appl. Math. E-Notes 9, 300-306 (2009).

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.

Reviewer: Aurel Spătaru (Bucureşti)

MSC:

60E15

Inequalities; stochastic orderings

Keywords:

tail probability; Pareto distribution; Fuk-Nagaev inequality