In a celebrated work by Hoeffding [J. Amer. Statist. Assoc. 58 (1963) 13-30], several inequalities for tail probabilities of sums Mn=X1+⋯ +Xn of bounded independent random variables Xj were proved.

This is a preview. Log in through your library . Abstract Let k > 0 be an integer and Y a standard Gamma(k) distributed random variable. Let X be an independent positive random variable with a density ...