Parametric inference in a perturbed gamma degradation process

TL;DR

This paper develops a method for estimating parameters in a gamma degradation process perturbed by Brownian motion, using moments estimation, and analyzes the estimators' properties with simulations and real data.

Contribution

It introduces a novel parameter estimation approach for a perturbed gamma degradation model and explores its asymptotic behavior with practical applications.

Findings

Estimators are consistent and asymptotically normal.

Method performs well in simulations and real data.

Derived explicit formulas for regular and irregular observation schemes.

Abstract

We consider the gamma process perturbed by a Brownian motion (independent of the gamma process) as a degradation model. Parameters estimation is studied here. We assume that $n$ independent items are observed at irregular instants. From these observations, we estimate the parameters using the moments method. Then, we study the asymptotic properties of the estimators. Furthermore we derive some particular cases of items observed at regular or non-regular instants. Finally, some numerical simulations and two real data applications are provided to illustrate our method.