Generalizations of Runs and Patterns Distributions for Sequences of Binary Trials

Spiros D Dafnis; Frosso S Makri; Markos V Koutras

doi:10.1007/s11009-020-09810-0

Generalizations of Runs and Patterns Distributions for Sequences of Binary Trials

Methodol Comput Appl Probab. 2021;23(1):165-185. doi: 10.1007/s11009-020-09810-0. Epub 2020 Jul 27.

Authors

Spiros D Dafnis¹, Frosso S Makri², Markos V Koutras¹

Affiliations

¹ Department of Statistics and Insurance Science, School of Finance and Statistics, University of Piraeus, Piraeus, Greece.
² Department of Mathematics, School of Natural Sciences, University of Patras, Patras, Greece.

Abstract

In the present paper we study the distributions of families of patterns which generalize runs and patterns distributions extensively examined in the literature during the last decades. In our analysis we assume that the sequence of outcomes under investigation includes independent, but not necessarily identically distributed trials. An illustration is also provided how our new results could be exploited to enrich a new system, still in research, related to patients' weaning from mechanical ventilation.

Keywords: Biomedical engineering; Exact distribution; Markov chain; Pattern; Run.