Abstract

Upper bounds are derived for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt. It is assumed that the range of each summand of S is bounded or bounded above. The bounds for Pr(S-ES> nt) depend only on the endpoints of the ranges of the smumands and the mean, or the mean and the variance of S. These results are then used to obtain analogous inequalities for certain sums of dependent random variables such as U statistics and the sum of a random sample without replacement from a finite population.

Citations

1580	An Introduction to Probability Theory and Its Applications. Volume II - Feller - 1971
404	Stochastic Processes - Doob - 1953
130	A class of statistics with asymptotically normal distribution - Hoeffding - 1948
128	D: On a test of whether one or two random variables is stochastically larger than the other. Ann Math Stat - Mann, Whitney - 1947
30	Some inequalities relating to the partial sum of binomial probabilities - Okamoto - 1958
21	Consistency and unbiasedness of certain nonparametric tests - Lehmann - 1951
4	les valeurs limites des intégrales - Tchébychef, Sur
3	Probability inequalities of the Tchebycheff type - Savage - 1961
1	Probability inequalities for the sum of independent random variables - George - 1962
1	An extremal problem in probability theory" - - (Russian; English summary), Teoriya Veroyatnostei i ee Primeneniya - unknown authors - 1959