Monte Carlo Comparison of the Parameter Estimation Methods for the Two-Parameter Gumbel Distribution

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Aydin D., ŞENOĞLU B.

JOURNAL OF MODERN APPLIED STATISTICAL METHODS, cilt.14, sa.2, ss.123-140, 2015 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 14 Sayı: 2
  • Basım Tarihi: 2015
  • Doi Numarası: 10.22237/jmasm/1446351060
  • Dergi Adı: JOURNAL OF MODERN APPLIED STATISTICAL METHODS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.123-140
  • Anahtar Kelimeler: Gumbel distribution, estimation methods, Monte Carlo simulation, efficiency
  • Ankara Üniversitesi Adresli: Evet

Özet

The performances of the seven different parameter estimation methods for the Gumbel distribution are compared with numerical simulations. Estimation methods used in this study are the method of moments (ME), the method of maximum likelihood (ML), the method of modified maximum likelihood (MML), the method of least squares (LS), the method of weighted least squares (WLS), the method of percentile (PE) and the method of probability weighted moments (PWM). Performance of the estimators is compared with respect to their biases, MSE and deficiency (Def) values via Monte-Carlo simulation. A Monte Carlo Simulation study showed that the method of PWM was the best performance the other methods of bias criterion and the method of ML outperforms the other methods in terms of Def criterion. A real life example taken from the hydrology literature is given at the end of the paper.