Inverted Modified Lindley Dağılımı için Parametre Tahmin Yöntemlerinin Karşılaştırılması

Abstract

Inverted Modified Lindley (IML) dağılımının, üstel ve Lindley dağılımlarına kıyasla daha iyi uyum sağlama yetenekleri gösterdiği önceki çalışmalarala gösterilmiştir. Bu çalışma, En Küçük Kareler (LS), Cramer von Misses (CvM) ve Maksimum Olabilirlik (ML) yöntemlerini kullanarak Inverted Modified Lindley (IML) dağılımının parametre tahminini incelemektedir. IML dağılımına ait parametrenin tahmin edilmesinde ML, LS ve CvM yöntemlerinin etkinliğini karşılaştırmak amacıyla bir Monte Carlo simülasyon çalışması yapılmıştır. Ayrıca ilgili tahmin yöntemleri kullanılarak çeşitli alanlardan gerçek veri uygulamaları sağlanmıştır. Bu yöntemlerin uyum performansı, ortalama karekök hata, belirleme katsayısı ve Kolmogorov-Smirnov testi kullanılarak değerlendirilmiştir. Uygulama sonuçlarına göre CvM metodu, IML dağılımı için dikkate alınan verileri daha bir iyi şekilde tanımlarken, simülasyon çalışması için ise, ML tahmin yöntemi öne çıkmaktadır.

Keywords

• Cramer von Missess
• En küçük kareler
• En çok olabilirlik
• Inverted Modified Lindley

A Comparison of Parameter Estimation Methods for the Inverted Modified Lindley Distribution

Abstract

The Inverted Modified Lindley (IML) distribution has been shown to exhibit superior fitting capabilities compared to the exponential and Lindley distributions. This study investigates the parameter estimation of the IML distribution using the Least Squares (LS), Cramer von Misses (CvM), and Maximum Likelihood (ML) methods. A Monte Carlo simulation study is conducted to compare the efficiency of the ML, LS, and CvM methods in estimating the parameters of the IML distribution. Moreover, real data applications from various fields are provided using related estimation methods. The fitting performance of these methods is evaluated using root mean squared error, coefficient of determination, and the Kolmogorov-Smirnov test. According to the application results, the CvM estimates describe the considered data for the IML distribution best, while the simulation study favors ML estimation among the considered methods.

Keywords

• Cramer von Missess
• Estimation
• Inverted Modified Lindley
• Least Squares
• Maximum Likelihood

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