A note on sums of independent random variables

Paweł Hitczenko, Stephen Montgomery-Smith

Published 1998-04-14, updated 1999-12-03Version 2

In this note a two sided bound on the tail probability of sums of independent, and either symmetric or nonnegative, random variables is obtained. We utilize a recent result by Lata{\l}a on bounds on moments of such sums. We also give a new proof of Lata{\l}a's result for nonnegative random variables, and improve one of the constants in his inequality.