Methodology and Computing in Applied Probability

, Volume 14, Issue 2, pp 383–403

Simulation and Estimation for the Fractional Yule Process

Article

DOI: 10.1007/s11009-010-9207-6

Cite this article as:
Cahoy, D.O. & Polito, F. Methodol Comput Appl Probab (2012) 14: 383. doi:10.1007/s11009-010-9207-6

Abstract

In this paper, we propose some representations of a generalized linear birth process called fractional Yule process (fYp). We also derive the probability distributions of the random birth and sojourn times. The inter-birth time distribution and the representations then yield algorithms on how to simulate sample paths of the fYp. We also attempt to estimate the model parameters in order for the fYp to be usable in practice. The estimation procedure is then tested using simulated data as well. We also illustrate some major characteristics of fYp which will be helpful for real applications.

Keywords

Yule–Furry processFractional calculusMittag–LefflerWrightPoisson processBirth process

AMS 2000 Subject Classifications

37A5062M8697K60

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Program of Mathematics and Statistics, College of Engineering and ScienceLouisiana Tech UniversityRustonUSA
  2. 2.Dipartimento di Scienze StatisticheSapienza University of RomeRomeItaly