Genetik Algoritma ile İlerleyen Tür Tip 2 Sansürlü Örneklemlerde Weibull Dağılımının Parametrelerinin En Çok Olabilirlik Tahmini

Bu çalışmada Weibull dağılımına sahip ilerleyen tür tip 2 sansürlü örneklemlerde parametre tahmini probleminde Newton yöntemine alternatif bir çözüm önerilmiştir. Newton yöntemi en çok olabilirlik tahmininde sıklıkla kullanılmaktadır. Newton yöntemi popüler olmasına rağmen en büyük dezavantajı en az iki kez türevlenebilir fonksiyonlar için kullanılabilmesidir. Olabilirlik fonksiyonu sansürlü örneklemlerde tam örneklemlere göre fonksiyonel olarak daha kompleks bir yapıda olduğundan, türev ve diğer hesaplamalar nispeten daha karışıktır. Bu çalışmada en çok olabilirlik yönteminde elde edilen denklem sisteminin çözümü için Newton metodunun kullanımındaki kısıtlamalara bir alternatif olarak Genetik Algoritma önerilmiştir. Detaylı bir simülasyon çalışması yardımıyla yan ve hata kareler ortalaması ile iki yöntemin performansları değerlendirilmiştir. Simülasyon sonuçlarına göre önerilen yöntemin karşılaştırılan tüm durumlar için ölçek parametresi için daha iyi sonuçlar verdiği, şekil parametresi için ise yanlar açısından sonuçların benzer olduğu ancak hata kareler ortalamasına göre bazı sansür şemaları için Newton yönteminin iyi sonuç verdiği bulunmuştur.

Maximum Likelihood Estimation of the Parameters of Progressively Type-2 Censored Samples From Weibull Distribution Using Genetic Algorithm

In this study we suggested an alternative solution to the parameter estimation problem of the Weibull distribution based on progressively Type-II censored samples with Newton method. Newton is one of the widely used methods for solving the system of equations especially in maximum likelihood estimation. Even though it is popular, the biggest disadvantage of the Newton method is that it is a valid method for only functions that derivativable at least two times. Since the likelihood functions are in more complex form for censored samples than in full samples, calculations of derivatives and related processes are more complicated. We proposed to use the Genetic Algorithm an alternative to the limitations of the Newton method in solution of system of equations in maximum likelihood estimation. Performance of these methods are evaluated by the simulated bias and mean square error criteria by an intensive simulation study. Simulation results of the study showed that the suggested method give better results than Newton method for scale parameter for all conditions. Also shape parameter results for simulated biases are similar for GA and Newton method but Newton has better mean squared error values for some censoring schemes.

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