On the monotonicity of tail probabilities

Robbert Fokkink, Symeon Papavassiliou, Christos Pelekis

Research output: Contribution to journalArticleScientificpeer-review

61 Downloads (Pure)

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 languageEnglish
Pages (from-to)133-141
Number of pages9
JournalProbability and Mathematical Statistics
Volume42
Issue number1
DOIs
Publication statusPublished - 2022

Keywords

  • (negative) binomial distribution
  • Poisson distribution
  • Simmons’ inequality
  • sums of independent random variables
  • tail comparisons

Fingerprint

Dive into the research topics of 'On the monotonicity of tail probabilities'. Together they form a unique fingerprint.

Cite this