Topp-Leone Nadarajah Haghighi Dağılımı

Year 2017, Volume: 10 Issue: 2, 119 - 127, 30.12.2017

Haitham M. Yousof , Mustafa Ç. Korkmaz

Abstract

Bu çalışmada yaşam verileri, güvenirlik problemleri ve yorulma ömrü çalışmalarında kullanılabilecek üç parametreli bir model üzerinde çalışılmıştır. Bu modele ait momentler, üreten fonksiyonlar, tamamlanmamış momentler ve sıra istatistikleri gibi istatistiksel ve matematiksel özellikler türetilmiştir. Tam örneklem durumuna dayalı olarak, model parametrelerinin sıradan en çok olabilirlik tahminleri elde edilmiştir. Bir simülasyon çalışması ile model parametrelerinin en çok olabilirlik tahmin edicilerinin performansları, standart sapma, yan ve hata kareler ortalamaları ile değerlendirilmiştir. Modelin kullanışlılığı, bir gerçek veri setine dayalı olarak gösterilmiştir. Önerilen dağılım bazı karşılaştırma kriterleri altında, literatürde iyi iyi bilinen birtakım dağılımlardan daha iyi uyum sağlamıştır.

Keywords

Topp-Leone dağılımı, Nadarajah-Haghighi dağılımı, en çok olabilirlik tahmini; genişletilmiş dağılımlar

Topp-Leone Nadarajah-Haghighi distribution

Abstract

In this paper, a three parameter model which can be used in modeling survival data, reliability problems and fatigue life studies has been studied. We derived explicit expressions for some of its statistical and mathematical identifying properties such as ordinary moments, generating function, incomplete moments and order statistics. The maximum likelihood estimations of model parameters were also obtained -being based on complete sample. We assessed the performance of the maximum likelihood estimators in terms of standard deviations, bias and mean squared errors by means of a simulation study. The usefulness of the model was illustrated by using a real data set. The proposed distribution provides better fits than some well-known generalized distributions under the same criteria of comparison.

Keywords

Topp-Leone distribution, Nadarajah-Haghighi distribution, maximum likelihood estimation, extended distributions

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