Weibull modeline uygulamalar içeren genelleştirilmiş dağıtımların Libby-Novick beta sınıfı için yeni bir kapalı form.

Yıl 2021, Cilt: 2 Sayı: 1, 23 - 42, 30.06.2021

Mohamed Ahmed

https://doi.org/10.52693/jsas.936902

Öz

Matematiksel özelliklerin türetilmesinde, rastgele sayıların üretilmesinde ve gerçek veri setlerinin uygulanmasında daha iyi esneklik elde etmek için kapalı forma sahip olmayan sınıflar yerine basit bir kapalı forma sahip yeni dağıtım sınıfları türetmek yararlıdır. Bu makalede, değiştirilmiş Libby-Novick (MLN) sınıfı olarak adlandırılan genelleştirilmiş dağıtımların yeni bir kapalı form sınıfı, Libby-Novick beta sınıfının örtük formundan türetilmiştir. İki önemli dağıtım sınıfı, MLN sınıfı tarafından yuvalanmıştır. Bazı genelleştirilmiş matematiksel özellikler türetilmiş ve maksimum olabilirlik tahmini (MLE) yöntemi kullanılarak MLN sınıfı parametreleri tahmini elde edilmiştir. MLN-Weibull (MLN-W) dağılımının tahminci davranışını araştırmak için önyükleme yaklaşımını kullanan bir simülasyon çalışması uygulanmıştır. MLN-W'nin potansiyelini göstermek için gerçek bir veri seti kullanılır.

Anahtar Kelimeler

yeni biçim Libby-Novick dağılımı, momentler, sıra istatistikleri, maksimum olasılık tahmini.

A new closed form for Libby-Novick beta class of generalized distributions with applications to Weibull model.

Öz

It is useful to derive new classes of distributions having a simple closed form instead of classes having no closed form to get better flexibility in deriving mathematical properties, generating random numbers and applying real data sets. In this paper, a new closed form class of generalized distributions, so-called the modified Libby-Novick (MLN) class, is derived from the implicit form of Libby-Novick beta class. Two important classes of distributions are nested by the MLN class. Some generalized mathematical properties are derived and the MLN class parameters estimation using maximum likelihood estimation (MLE) method is obtained. A simulation study using bootstrapping approach is applied to investigate the estimators behavior of the MLN-Weibull (MLN-W) distribution. A real data set is used to illustrate the potentiality of the MLN-W

Anahtar Kelimeler

the new form Libby-Novick distribution, moments, order statistics, maximum likelihood estimation.

Kaynakça

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