Ek Parametre İçermeyen Dönüşüm Tekniklerinin Karşılaştırılması ve İki Veri Seti Üzerinde Modellenmesi

Year 2024, Volume: 14 Issue: 3, 1444 - 1455, 15.09.2024

Hasan Hüseyin Gül

https://doi.org/10.31466/kfbd.1472795

Abstract

İstatistik literatüründe, yeni dağılım elde etmek için bazı teknikler geliştirilmiştir. Geliştirilen bu teknikler, var olan dağılıma yeni bir veya birkaç parametre ekleyerek oluşturulmaktadır. Parametre eklemek esneklik bağlamında olumlu bir etki yaratırken, parametre tahmini ve diğer istatistiksel çıkarımlarda işlem zorluğunu da beraberinde getirmektedir. Bu noktada son yıllarda araştırmacılar tarafından ek parametre içermeyen yeni dağılım üretme teknikleri önerilmeye başlanmıştır. Bu çalışmada, Dinesh-Umesh-Sanjay (DUS), Logaritmik dönüşüm (LT) ve Kavya-Manoharan (KM) teknikleri ele alınmış ve bu tekniklerin önerilen üstel dağılım versiyonları (DUSE, LTE, KME) üzerinde durulmuştur. Bu dağılımların r. momentleri, moment çıkaran fonksiyonları ve quantile fonksiyonları gibi istatistiksel özellikleri ve en çok olabilirlik tahminleri incelenmiştir. Ayrıca iki veri seti üzerinde tekniklerin modelleme yetenekleri karşılaştırılmıştır. Sonuç olarak, KM tekniği kullanılarak önerilen KME dağılımının iki veri setini de daha iyi modellediği görülmüştür.

Keywords

Dönüşüm Teknikleri, İstatistiksel Özellikler, En Çok Olabilirlik Tahmini, Üstel Dağılım

Comparison of Additional Parameter-Free Transformation Techniques and Modelling on Two Data Sets

Abstract

In the statistics literature, some techniques have been developed to obtain new distributions. These techniques are created by adding one or more parameters to the existing distribution. While adding parameters creates a positive effect in terms of flexibility, it also brings processing difficulties in parameter estimation and other statistical inferences. At this point, new distribution generation techniques without additional parameters have been proposed by researchers in recent years. In this study, Dinesh-Umesh-Sanjay (DUS), Logarithmic transformation (LT) and Kavya-Manoharan (KM) techniques are discussed and the proposed exponential distribution versions of these techniques (DUSE, LTE, KME) are examined. Statistical properties of these distributions such as r. moments, moment generating functions, quantile functions and maximum likelihood estimates are analysed. In addition, the modelling capabilities of the techniques are compared on two data sets. As a result, it was found that the KME distribution proposed using the KM technique modelled both data sets better.

Keywords

Transformation techniques, Statistical properties, Maximum likelihood estimation, Exponential distribution

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