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New maximal inequalities for N-demimartingales with scan statistic applications

Part of: Distribution theory - Probability Stochastic processes

Published online by Cambridge University Press:  22 June 2017

Markos V. Koutras  and
Demetrios P. Lyberopoulos
Markos V. Koutras*
Affiliation:
University of Piraeus
Demetrios P. Lyberopoulos*
Affiliation:
University of Piraeus
*
* Postal address: Department of Statistics and Insurance Science, University of Piraeus, 80 Karaoli and Dimitriou Street, 185 34 Piraeus, Greece.
* Postal address: Department of Statistics and Insurance Science, University of Piraeus, 80 Karaoli and Dimitriou Street, 185 34 Piraeus, Greece.
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Abstract

In the present work, some new maximal inequalities for nonnegative N-demi(super)martingales are first developed. As an application, new bounds for the cumulative distribution function of the waiting time for the first occurrence of a scan statistic in a sequence of independent and identically distributed (i.i.d.) binary trials are obtained. A numerical study is also carried out for investigating the behavior of the new bounds.

Keywords

N-demimartingaleN-demisupermartingaledemimartingalescan statisticdemisubmartingaleboundi.i.d. binary trials

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 60G48: Generalizations of martingales

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 2 , June 2017 , pp. 363 - 378
Copyright
Copyright © Applied Probability Trust 2017 

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