A STUDY ON COMPARISONS OF BAYESIAN AND CLASSICAL PARAMETER ESTIMATION METHODS FOR THE TWO-PARAMETER WEIBULL DISTRIBUTION

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Yılmaz A., Kara M., AYDOĞDU H.

COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, cilt.69, sa.1, ss.576-602, 2020 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 69 Sayı: 1
  • Basım Tarihi: 2020
  • Doi Numarası: 10.31801/cfsuasmas.606890
  • Dergi Adı: COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.576-602
  • Anahtar Kelimeler: Bayes approximation, parameter estimation, new estimator, L-moment estimator, simulation study, LEAST-SQUARES ESTIMATION, MAXIMUM-LIKELIHOOD, SHAPE PARAMETER, DESCRIBE, MOMENT, MODEL, RISK
  • Ankara Üniversitesi Adresli: Evet

Özet

The main objective of this paper is to determine the best estimators of the shape and scale parameters of the two parameter Weibull distribution. Therefore, both classical and Bayesian approximation methods are considered. For parameter estimation of classical approximation methods maximum likelihood estimators (MLEs), modified maximum likelihood estimators-I (MMLEs-I), modified maximum likelihood estimators-II (MMLEs-II), least square estimators (LSEs), weighted least square estimators (WLSEs), percentile estimators (PEs), moment estimators (MEs), L-moment estimators (LMEs) and TL-moment estimators (TLMEs) are used. Since the Bayesian estimators don't have the explicit form. There are Bayes estimators are obtained by using Lindley's and Tierney Kadane's approximation methods in this study. In Bayesian approximation, the choice of loss function and prior distribution is very important. Hence, Bayes estimators are given based on both the non-informative and informative prior distribution. Moreover, these estimators have been calculated under different symmetric and asymmetric loss functions. The performance of classical and Bayesian estimators are compared with respect to their biases and MSEs through a simulation study. Finally, a real data set taken from Turkish State Meteorological Service is analysed for better understanding of methods presented in this paper.