Dönüştürülmüş Birim Üstel Yarı Lojistik Dağılım ve Uygulamaları

Year 2024, , 249 - 260, 31.12.2024

Murat Genç , Ömer Özbilen

https://doi.org/10.54370/ordubtd.1512101

Abstract

Orantılı tehlike hızı model ailesinin bir üyesi olan birim üstel yarı lojistik dağılım temel dağılım olarak kullanılarak, dönüştürülmüş (transmuted) birim üstel yarı lojistik dağılım olarak adlandırılan yeni bir dağılım önerilmiştir. Önerilen dağılımın momentler, moment çıkaran fonksiyon, kantil fonksiyonu ve stres-mukavemet güvenilirliği gibi istatistiksel özellikleri bu çalışmada ayrıntılı olarak incelenmiştir. Dağılım parametrelerinin istatistiksel çıkarımı için maksimum olabilirlik tahmin yöntemi tartışılmıştır. Maksimum olabilirlik tahminlerinin çeşitli koşullar altındaki davranışını araştırmak için yeni dağılıma dayalı bir simülasyon çalışması yapılmıştır. Ayrıca, bir başarısızlık-zaman veri kümesi üzerinde dağılımın performansını göstermek için sayısal bir örnek sunulmuştur.

Keywords

dönüştürülmüş dağılım ailesi, UEHL dağılımı, başarısızlık zamanları, maksimum olabilirlik tahmincisi, veri analizi

Transmuted Unit Exponentiated Half-Logistic Distribution and its Applications

Abstract

A novel distribution, termed the transmuted unit exponentiated half-logistic distribution, has been proposed using the unit exponential half-logistic distribution, a member of the proportional hazard rate model family, as the base distribution. The statistical characteristics of the proposed distribution, including moments, moment-generating function, quantile function, and stress-strength reliability, have been thoroughly examined in this study. The maximum likelihood estimation method has been discussed for statistical inference of the distribution parameters. A simulation study based on the new distribution has been conducted to investigate the behavior of maximum likelihood estimates under various conditions. In addition, a numerical example has been presented to illustrate the performance of the distribution on a failure-time dataset.

Keywords

transmuted family, UEHL distribution, failure times, maximum likelihood estimator, data analysis

Ethical Statement

There are no ethical issues related to the publication of this article.

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