Discrimination of the Gamma, Weibull and Log-Normal Distributions According to Probability of Correct Selection

Year 2012, Volume: 9 Issue: 1, 11 - 20, 13.07.2012

Hayrinisa Demirci Biçer Cemal Atakan

Abstract

Gamma, Weibull and Log-Normal distributions are often used distributions for modelling skewed data. In this study, for a given data set the problem of selecting Gamma, Weibull or Log-Normal distributions is focused on for the modelling. Distribution of a given set of data, Gamma, Weibull or Log-Normal distribution has been decided by the probability of correct selection that is calculated by constructing Monte-Carlo simulations and asymptotic results under the null hypothesis.

Keywords

Probability of correct selection, Gamma distribution, Log-Normal distribution, Likelihood ratio tests, Weibull distribution

Gamma, Weibull ve Log-Normal Dağılımlarının Doğru Seçim Olasılıklarına Göre Ayrıştırılması

Abstract

Gamma, Weibull ve Log-Normal dağılımları, çarpık verilerin analizi için sık kullanılan dağılımlardır. Bu çalışmada, verilen bir veri setinin, Gamma, Weibull ya da Log-Normal dağılımlardan hangisi ile modelleneceği problemi üzerinde durulmuştur. Verilen bir veri setinin dağılımının Gamma, Weibull ya da Log-Normal dağılımından hangisinden geldiğine, veri setinin dağılımının sırasıyla ilgili dağılımlara göre oluşturulan yokluk hipotezi altında Monte-Carlo simülasyonlan ve asimptotik sonuçlardan hesaplanan doğru seçim olasılıkları ile karar verilmiştir.

Keywords

Doğru seçim olasılığı, Gamma dağılımı, Log-Normal dağılım, Olabilirlik oranı, Weibull dağılımı

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