On the monotonicity of tail probabilities

• Autorzy: Fokkink Robbert , Pelekis Christos , Papavassiliou Symeon

Identyfikatory

DOI

10.37190/0208-4147.00050

• Języki publikacji: EN

Abstrakty

EN

Let S and X be independent random variables, assuming values in the set of non-negative integers, and suppose further that both expectations ES and EX are integers satisfying ES>EX. We establish a sufficient condition for the tail probability P(S> ES) to be larger than the tail probability P(S+X> E(S+X)), when the mean of S is equal to the mode.

Słowa kluczowe

EN

tail comparisons; sums of independent random variables; (negative) binomial distribution; Poisson distribution; Simmons' inequality

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2022
• Tom: Vol. 42, Fasc. 1
• Strony: 133--141
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Fokkink Robbert

• Institute of Applied Mathematics, Delft University of Technology, Mourikbroekmanweg 6, 2628 XE Delft, The Netherlands

autor

Pelekis Christos

• School of Electrical and Computer Engineering, National Technical University of Athens, Zografou, Athens, Greece, 15780

autor

Papavassiliou Symeon

• School of Electrical and Computer Engineering, National Technical University of Athens, Zografou, Athens, Greece, 15780

Bibliografia

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• 3. K. Jogdeo and S. M. Samuels, Monotone convergence of binomial probabilities and a generalization of Ramanujan's equation, Ann. Math. Statist. 39 (1968), 1191-1195.
• 4. J. M. Kane, Monotonic approach to central limits, Proc. Amer. Math. Soc. 129 (2000), 2127-2133.
• 5. O. Perrin and E. Redside, Generalization of Simmons' theorem, Statist. Probab. Lett. 77 (2007), 604-606.
• 6. T. C. Simmons, A new theorem in probability, Proc. London Math. Soc. 1 (1894), 290-325.
• 7. H. Teicher, An inequality on Poisson probabilities, Ann. Math. Statist. 26 (1955), 147-149.