ESTIMATING THE PARAMETERS OF GENERALIZED LOGISTIC DISTRIBUTION VIA GENETIC ALGORITHM BASED ON REDUCED SEARCH SPACE

YALÇINKAYA A., Kılıç A., ŞENOĞLU B.

Journal of Mathematical Sciences (United States), 2024 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1007/s10958-024-07088-y
  • Dergi Adı: Journal of Mathematical Sciences (United States)
  • Derginin Tarandığı İndeksler: Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Anahtar Kelimeler: Efficiency, Generalized logistic, Genetic algorithm, Maximum likelihood, Modified maximum likelihood, Newton–Raphson
  • Ankara Üniversitesi Adresli: Evet

Özet

In this study, maximum likelihood (ML) estimates of the parameters of generalized logistic (GL) distribution are obtained using the genetic algorithm (GA) based on the reduced search space (RSS) proposed by (Yalçınkaya et al. Swarm and Evolutionary Computation 38, 127–138, 2018). RSS is defined in terms of the confidence intervals based on modified maximum likelihood (MML) estimators. MML estimators are the explicit functions of the sample observations and asymptotically equivalent to the ML estimators, (Tiku, Biometrika 54, 155–165, 1967). To see the effectiveness of RSS, we examine the performance of GA based on RSS against GA based on fixed search space (FSS). The efficiencies of these estimators are also compared with the classical ML estimators using Newton–Raphson (NR) algorithm via Monte Carlo simulation study. MML estimators of GL distribution parameters are also included into the study to show the performance of the non-iterative MML methodology against the iterative ML methodology. At the end of the study, a real-life example is given to see the implementation of the proposed methodology.