Svante Janson
Published 2016-09-02Version 1
A survey is given of some Chernoff type bounds for the tail probabilities P(X-EX > a) and P(X-EX < a) when X is a random variable that can be written as a sum of indicator variables that are either independent or negatively related. Most bounds are previously known and some comparisons are made. This paper was written in 1994, but was never published because I had overlooked some existing papers containing some of the inequalities. Because of some recent interest in one of the inequalities, which does not seem to be published anywhere else, it has now been lightly edited and made available here.
Bounds on Tail Probabilities in Exponential families
Tail probabilities of St. Petersburg sums, trimmed sums, and their limit
Bounds for tail probabilities of martingales using skewness and kurtosis
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