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.
Original language | English |
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Pages (from-to) | 133-141 |
Number of pages | 9 |
Journal | Probability and Mathematical Statistics |
Volume | 42 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2022 |
Keywords
- (negative) binomial distribution
- Poisson distribution
- Simmons’ inequality
- sums of independent random variables
- tail comparisons