Simulation and estimation for the fractional Yule process

TL;DR

This paper introduces the fractional Yule process, providing its representations, distributions, simulation algorithms, and parameter estimation methods, demonstrating its practical applicability through simulations.

Contribution

It presents new representations, simulation algorithms, and estimation procedures for the fractional Yule process, enhancing its practical usability.

Findings

Derived probability distributions for the process

Developed algorithms for simulating sample paths

Validated estimation procedures with simulated data

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.