Odd Genelleştirilmiş Yarı Lojistik Weibull-Rayleigh Dağılımı: Özellikleri ve Bir Uygulama

Year 2022, , 307 - 314, 30.04.2022

Ceren Ünal , Gamze Özel

https://doi.org/10.35414/akufemubid.1068310

Abstract

Bu çalışmada yeni bir dağılım olan üç parametreli Odd genelleştirilmiş yarı lojistik Weibull-Rayleigh (OGYLW-R) dağılımı tanıtılmıştır. Dağılımın elde edilmesinde, Chipepa vd. (2020) tarafından önerilen yeni dağılım ailesi olarak Odd genelleştirilmiş yarı lojistik Weibul-genelleştirilmiş (OGYLW-G) dağılım ailesi kullanılmıştır. Elde edilen dağılımın olasılık yoğunluk, dağılım, hazard, yaşam ve kantil fonksiyonları, momentleri, çarpıklık, basıklık katsayıları ve sıralı istatistiklerini içeren temel istatistiksel özellikleri elde edilmiştir. Dağılımın parametre tahmini en çok olabilirlik tahmin yöntemi ile bulunmuştur. Önerilen dağılımın literatürdeki dağılımlardan üstünlüğünü göstermek için gerçek veri setine uygulanmış ve OGYLW-R dağılımının kesilmiş Weibull-Rayleigh dağılımının uyumu ile karşılaştırılmıştır. OGHLW-R dağılımının veriye daha uyumlu olduğu görülmüştür. Çarpıklık katsayısına göre dağılımın sola çarpık, basıklık katsayısına göre ise normal dağılıma göre daha basık olduğu görülmüştür.

Keywords

Hazard fonksiyonu, En çok olabilirlik tahmin yöntemi, Weibull dağılımı, Rayleigh dağılımı

Odd Generalized Half-Logistic Weibull Rayleigh Distribution: Properties and an Application

Abstract

In this study, a new three-parameter Odd generalized semi-logistic Weibull-Rayleigh (OGYLW-R) distribution is introduced. In obtaining the distribution, Chipepa et al. (2020), the Odd generalized semi-logistic Weibul-generalized (OGYLW-G) distribution family was used as the new distribution family. Basic statistical properties of the obtained distribution including probability density, distribution, hazard, survival and quantile functions, moments, skewness, kurtosis coefficients, and ordinal statistics are obtained. The parameter estimation of the distribution was found using the maximum likelihood estimation method. To show the superiority of the proposed distribution over the distributions in the literature, it was applied to the real data set and the OGYLW-R distribution was compared with the fit of the truncated Weibull-Rayleigh distribution. It was seen that the OGHLW-R distribution was more compatible with the data. According to the skewness coefficient, it was observed that the distribution was skewed to the left, and according to the kurtosis coefficient, it was more flattened than the normal distribution.

Keywords

Hazard function, Maximum likelihood estimation method, Weibull distribution, Rayleigh distribution

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