Browsing by Author "Kara, Mahmut"

Now showing 1 - 3 of 3
  • No Thumbnail Available
    Item
    A study on comparisons of Bayesian and classical parameter estimation methods for the two-parameter Weibull distribution
    (Ankara Üniversitesi Fen Fakültesi, 2020-06-30) Yılmaz, Asuman; Kara, Mahmut; Aydoğdu, Halil; İstatistik; Fen Fakültesi
    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.
  • No Thumbnail Available
    Item
    Alfa seri süreçlerde parametre tahmini
    (Fen Bilimleri Enstitüsü, 2014) Kara, Mahmut; Aydoğdu, Halil; İstatistik
    Stokastik modellemede sık kullanılan alfa seri süreçlerde parametre tahmin problemi ile karşılaşılmaktadır. Bir alfa seri süreçte ilk olayın gerçekleşme zamanının dağılım fonksiyonu F ile gösterilsin. Bu çalışmada F 'nin bilinmemesi durumunda alfa seri sürecin parametresi ve dağılımının ortalama ve varyansı için lineer regresyon yöntemi kullanılarak bazı parametrik olmayan tahmin ediciler verilir. Bu parametreler için F sırasıyla Weibull, gama ve lognormal dağılım fonksiyonu iken en çok olabilirlik ve uyarlanmış en çok olabilirlik yöntemi ile parametrik tahmin ediciler elde edilir. Bu tahmin edicilerin tutarlılık ve asimptotik normallik özellikleri incelenir. Ayrıca tahmin edicilerin işlerlikleri bir simülasyon çalışması ile değerlendirilir.
  • No Thumbnail Available
    Item
    Statistical inference for geometric process with the Rayleigh distribution
    (Ankara Üniversitesi, 2019-02-01) Aydoğdu, Halil; Biçer, Cenker; Kara, Mahmut; Biçer, Hayrinisa Demirci; İstatistik; Fen Fakültesi
    The aim of this study is to investigate the solution of the statistical inference problem for the geometric process (GP) when the distribution of first occurrence time is assumed to be Rayleigh. Maximum likelihood (ML) estimators for the parameters of GP, where a and λ are the ratio parameter of GP and scale parameter of Rayleigh distribution, respectively, are obtained. In addition, we derive some important asymptotic properties of these estimators such as normality and consistency. Then we run some simulation studies by different parameter values to compare the estimation performances of the obtained ML estimators with the non-parametric modified moment (MM) estimators. The results of the simulation studies show that the obtained estimators are more efficient than the MM estimators.