Generalizations of Runs and Patterns Distributions for Sequences of Binary Trials

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.