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The joint characterization of discrete and continuous “waiting times” through their reciprocal relationships

TítuloThe joint characterization of discrete and continuous “waiting times” through their reciprocal relationships
Publication TypeUnpublished
Year of Publication2005
AuthorsCoelho CA
Series TitlePreprint
AbstractLet us suppose there is an event C (occurrence of a given defect or disease) that is part of a group of events we are interested in, and whose probability of occurrence in that group is known. The distribution of the waiting times for the r1-th event in that group, given that we expect r events C, and the distribution of the number of events in the group that not C, given that we waited for a length y, waiting for r1 events in the group, given that we expected r events C, are derived based on very mild assumptions. Relations of the distributions obtained with known distributions, their expression as mixtures and a limiting case are also studied. Cases where r1r are studied in detail, since they correspond to two different situations of interest, the one in which the event C is one of the the rarest ones in its group, is not easy to identify or its occurrence r times kills or disables the observation unit, or the case in which it may be rather common in the group and easy to identify. Examples of application in epidemiology, industry, transportation and agriculture are used for illustration.
URLhttp://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2005/23_05.pdf