Estimation of the parameters of the gamma geometric process


Kara M. , GÜVEN G., ŞENOĞLU B., AYDOĞDU H.

JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, 2022 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Publication Date: 2022
  • Doi Number: 10.1080/00949655.2022.2040501
  • Title of Journal : JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION
  • Keywords: Geometric process, gamma distribution, modified maximum likelihood, asymptotic normality, Monte Carlo simulation, STATISTICAL-INFERENCE, MODEL, SYSTEM

Abstract

There is no doubt that finding the estimators of model parameters accurately and efficiently is very important in many fields. In this study, we obtain the explicit estimators of the unknown model parameters in the gamma geometric process (GP) via the modified maximum likelihood (MML) methodology. These estimators are as efficient as maximum likelihood (ML) estimators. The marginal and joint asymptotic distributions of the MML estimators are also derived and efficiency comparisons between ML and MML estimators are made through an extensive Monte Carlo simulations. Moreover, a real data example is considered to illustrate the performances of the MML estimators together with their ML counterparts. According to simulation results, the performances of MML and ML estimators are close to each other even for small sample sizes.