Yeni Kumaraswamy genişletilmiş Garima dağılımı istatistiksel özellikleri ve uygulaması

Year 2023, Volume: 16 Issue: 2, 116 - 146, 31.12.2023

Ayşe Metin Karakaş , Murat Karakaş , Mine Doğan

Abstract

Bu makale yeni bir Kumaraswamy Genişletilmiş Garima dağıLım ailesini sunmayı amaçlamaktadır. Kümülatif bir dağılım fonksiyonu, başarısızlık oranı, risk oranı, ters risk fonksiyonu, tek fonksiyon, kümülatif risk fonksiyonu, moment r-th, moment üreten fonksiyonun karakteristik fonksiyonu, momentler, ortalama ve varyans, Lorenz ve Bonferroni eğrileri, sıra istatistikleri, MLE, arızalar arasındaki ortalama süre (MTBF), Renyi ve Tsallis entropileri gibi özellikleri elde ettik. MLE tekniği, yeni Kumaraswamy Extended Garima dağılımının parametrelerini tahmin eder. MLE tekniğinin parametreleri, doğrusal olmayan bir denklem sistemi ve Simetrik Bilgi Matrisi kullanılarak türetilir. Ayrıca sonuçlar olasılık dağılımları olduğundan diğerlerine benzer. Bulgulara göre, bu veri setlerine önerilen dağılım, mevcut olasılık dağılımlarından daha iyi uymaktadır.

Keywords

Garima dağılımı, Kumaraswamy dağılımı, Kümülatif dağılım fonksiyonu, Karakteristik fonksiyon, Simetrik bilgi matrisi.

The novel kumaraswamy extended garima distribution, statistical properties and its application

Abstract

This essay aims to present a novel Kumaraswamy Extended Garima distribution family. We obtain a cumulative distribution function, the failure rate, the risk rate, the inverse risk function, the odd function, the cumulative risk function, the moment r-th, the characteristic function of the moment generating function, the moments, the mean and the variance, Lorenz and Bonferroni curves, order statistics, MLE, mean time between failures (MTBF), Renyi and Tsallis entropies. The MLE technique estimates the parameters of the new Kumaraswamy Extended Garima distribution. The parameters of the MLE technique are derived using a nonlinear system of equations and the Symmetric Information Matrix. Furthermore, the consequences are analogous to others because they are probability distributions. According to the findings, the proposed distribution fits these data sets better than existing probability distributions.

Keywords

Garima distribution, Kumaraswamy distribution, Cumulative distribution function, Characteristic function, Symmetric information matrix.

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