Abstract:
We obtain new inequalities for values of jumps for discrete distribution functions. Values of jumps are bounded by linear combinations of a finite number of moments of the distributions. Obtained inequalities can be used for estimation of ranges for values of improbable jumps when frequencies are zero and are not interesting as estimators. We discuss relationships of derived inequalities with inequalities for probabilities of unions of events and the Caushy-Bunyakovski and Holder inequalities as well.
Keywords:Bonferroni inequalities, probabilities of unions of events, probabilities of combinations of events, Caushy-Bunyakovski inequality, Holder inequality, value of jump of distribution function.
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