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

Öz

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.

Anahtar Kelimeler

• 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

Öz

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.

Anahtar Kelimeler

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

Kaynakça

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