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Abstract Details

Activity Number: 72
Type: Contributed
Date/Time: Sunday, July 29, 2012 : 4:00 PM to 5:50 PM
Sponsor: Section on Statistical Computing
Abstract - #304499
Title: Statistical Methods for Fractional Birth and Fractional Death Processes
Author(s): Dexter Cahoy*+
Companies: Louisiana Tech University
Address: Math & Statistics Dept., COES, Ruston, LA, 71272, United States
Keywords: Poisson process ; Yule process ; birth and death processes ; Mittag-Leffler ; Renewal process

We study the statistical properties of some counting processes which are generalized using the techniques of fractional calculus. In particular, the generalizations of the standard Poisson, Yule process, and the death process called the fractional Poisson process, fractional birth process, and the fractional death process respectively, are examined. Note that these models allow both Markovian and non-Markovian behaviors.

Algorithms on how to estimate the parameters and simulate sample trajectories of these models are developed. More statistical properties are derived and generalizations are proposed. Open problems are also discussed.

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