On the monotonicity of tail probabilities
R.J. Fokkink (TU Delft - Delft Institute of Applied Mathematics, TU Delft - Applied Probability)
Symeon Papavassiliou (National Technical University of Athens)
Christos Pelekis (National Technical University of Athens)
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Abstract
Let S and X be independent random variables, assuming values in the set of non-negative integers, and suppose further that both E(S) and E(X) are integers satisfying E(S) ≥ E(X). We establish a sufficient condition for the tail probability P(S ≥ E(S)) to be larger than the tail P(S + X ≥ E(S + X)), when the mean of S is equal to the mode.