Simulation and Estimation for the Fractional Yule Process
- 154 Downloads
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.
KeywordsYule–Furry process Fractional calculus Mittag–Leffler Wright Poisson process Birth process
AMS 2000 Subject Classifications37A50 62M86 97K60
Unable to display preview. Download preview PDF.
- Cahoy DO (2007) Fractional poisson process in terms of alpha-stable densities. USAGoogle Scholar
- Kilbas AA, Srivastava HM, Trujillo JJ (2006) Theory and applications of fractional differential equations. Elsevier ScienceGoogle Scholar
- Paris RB, Kaminski D (2001) Asymptotics and Mellin–Barnes integrals. Cambridge University PressGoogle Scholar
- Podlubny I (1999) Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, some methods of their solution and some of their applications. Academic Press, San DiegoGoogle Scholar