STOCHASTIC MODELS FROM EVENT COUNT DATA
Abstract
In practice, information characterizing the interevent times (time lengths between consecutive events) of a process may be unavailable or difficult to obtain. On the other hand, the number of events per unit time (count data) are simple and economical to collect. In addition, the only information available in many situations consists of count data. In the last few years, there has been much research in the area of stochastic modeling using point processes by a varied group of researchers. Despite this extensive and diverse research effort, little attention has been given to modeling techniques that are based on event count data rather than event time data. In addition, the existing techniques based on count data are either too narrow in scope (for example, fit a Poisson process), employ limit theorem results, or provide unsatisfactory fits. In this work, a general framework for modeling processes given only count data is developed. In addition, an estimation procedure for the interevent time distribution of a renewal process from event count data is developed and examined. This estimation procedure performs best when the count data consists (primarily) of a sequence of zeros and ones.
Degree
Ph.D.
Subject Area
Industrial engineering
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