Estimation of the parameters of the gamma geometric process

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

JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, cilt.92, ss.2525-2535, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 92
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1080/00949655.2022.2040501
  • Dergi Adı: JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Business Source Elite, Business Source Premier, CAB Abstracts, Communication Abstracts, Metadex, Veterinary Science Database, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.2525-2535
  • Anahtar Kelimeler: Geometric process, gamma distribution, modified maximum likelihood, asymptotic normality, Monte Carlo simulation, STATISTICAL-INFERENCE, MODEL, SYSTEM
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

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.