Parameter estimation for fractional Poisson processes

TL;DR

This paper develops a formal parameter estimation method for the fractional Poisson process, enabling its practical application by establishing estimator properties and testing them with simulations.

Contribution

It introduces a new estimation procedure for the fractional Poisson process parameters and proves their asymptotic normality, facilitating confidence interval construction.

Findings

Establishes asymptotic normality of estimators

Provides confidence intervals for parameters

Validates estimators with simulated data

Abstract

The paper proposes a formal estimation procedure for parameters of the fractional Poisson process (fPp). Such procedures are needed to make the fPp model usable in applied situations. The basic idea of fPp, motivated by experimental data with long memory is to make the standard Poisson model more flexible by permitting non-exponential, heavy-tailed distributions of interarrival times and different scaling properties. We establish the asymptotic normality of our estimators for the two parameters appearing in our fPp model. This fact permits construction of the corresponding confidence intervals. The properties of the estimators are then tested using simulated data.