Parametric estimations of the mean value and variance functions in geometric process

Abstract

The paper introduces novel parametric estimators for the mean value function (MVF) and variance function (VF) in geometric processes (GPs) based on a random sample which belongs to a GP. Specifically, it addresses scenarios where the distribution function of the first interarrival time of GP is analytically known, but its parameters, along with the ratio parameter of the GP, are unknown. It establishes a solid theoretical foundation for the estimators proposed and investigates some statistical properties such as strong consistency and asymptotic unbiasedness of the estimators. These results generalize some of the findings acquired in previous studies. To evaluate the performance of the proposed estimators, we conduct a comprehensive Monte Carlo simulation study. This involves using various lifetime distributions, such as gamma, Weibull, and lognormal considering different sample sizes and parameter values. A discussion of an application to software engineering is also provided to illustrate the applicability of the methods developed in this study.