Estimation of Parameters for the Gumbel Type-I Distribution under Type-II Censoring Scheme

Yılmaz A., Kara M.

Baghdad Science Journal, cilt.20, sa.3, ss.834-842, 2023 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 20 Sayı: 3
  • Basım Tarihi: 2023
  • Doi Numarası: 10.21123/bsj.2022.6898
  • Dergi Adı: Baghdad Science Journal
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.834-842
  • Anahtar Kelimeler: Bayesian Methods, Gumbel Type-I Distribution, Simulation, Type -II Censoring
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

This paper aims to decide the best parameter estimation methods for the parameters of the Gumbel type-I distribution under the type-II censorship scheme. For this purpose, classical and Bayesian parameter estimation procedures are considered. The maximum likelihood estimators are used for the classical parameter estimation procedure. The asymptotic distributions of these estimators are also derived. It is not possible to obtain explicit solutions of Bayesian estimators. Therefore, Markov Chain Monte Carlo, and Lindley techniques are taken into account to estimate the unknown parameters. In Bayesian analysis, it is very important to determine an appropriate combination of a prior distribution and a loss function. Therefore, two different prior distributions are used. Also, the Bayesian estimators concerning the parameters of interest under various loss functions are investigated. The Gibbs sampling algorithm is used to construct the Bayesian credible intervals. Then, the efficiencies of the maximum likelihood estimators are compared with Bayesian estimators via an extensive Monte Carlo simulation study. It has been shown that the Bayesian estimators are considerably more efficient than the maximum likelihood estimators. Finally, a real-life example is also presented for application purposes.