BİRİM FAV-JERRY DAĞILIMI: ÖZELLİKLER VE UYGULAMALAR

Abstract

Bu makale yeni bir sınırlı istatistiksel dağılım sunmakta ve grafik gösterimler kullanılarak gösterilen kümülatif dağılım, olasılık yoğunluğu ve tehlike oranı fonksiyonları dahil olmak üzere temel özelliklerini araştırmaktadır. Çalışmada momentler, çarpıklık, basıklık, Bonferroni ve Lorenz eğrileri ve sıra istatistikleri gibi matematiksel özellikler incelenmektedir. Yeni modellerin bilinmeyen parametrelerine ilişkin tahminciler, Monte Carlo simülasyonlarında performans bias, ortalama karesel hatalar, ortalama mutlak bias ve ortalama bağıl hata üzerinden değerlendiriliyor. Son olarak, yeni modelin pratik uygulanabilirliği, iki gerçek veri analizi aracılığıyla gösterilmektedir.

Keywords

• Sınırlı İstatistiksel Dağılım
• Bonferroni ve Lorenz Eğrileri
• Moment Özellikleri
• Nokta Tahmini
• Toplam Süt Üretimi Oranı Verisi

UNIT FAV-JERRY DISTRIBUTION: PROPERTIES AND APPLICATIONS

Abstract

This paper introduces a novel bounded statistical distribution and explores its key characteristics, including cumulative distribution, probability density, and hazard rate functions, illustrated using graphical representations. The study examines mathematical properties such as moments, skewness, kurtosis, the Bonferroni and Lorenz curves, and order statistics. Estimators for the unknown parameter of new models are assessed, with performance evaluated via bias, mean square errors, average absolute bias, and mean relative error in Monte Carlo simulations. Finally, the practical utility of the new model is demonstrated through two real data analyses.

Keywords

• Bounded Statistical Distribution
• Bonferroni and Lorenz Curves
• Moment Properties
• Point Estimation
• Total Milk Production Proportion Data

References

1. Attia, I. M., “A Novel Unit Distribution Named as Median Based Unit Rayleigh (MBUR): Properties and Estimations”, arXiv preprint arXiv:2410.04132, 2024.
2. Maya, R., Jodra, P., Irshad, M. R. and Krishna, A., “The Unit Muth Distribution: Statistical Properties and Applications”, Ricerche di Matematica, 73, 4, 1843–1866, 2024.
3. Muhammad, M., Abba, B., Xiao, J., Alsadat, N., Jamal, F. and Elgarhy, M., “A New Three-Parameter Flexible Unit Distribution and Its Quantile Regression Model”, IEEE Access, 12, 156235–156251, 2024.
4. Ragab, I. E., Alsadat, N., Balogun, O. S. and Elgarhy, M., “Unit Extended Exponential Distribution with Applications”, Journal of Radiation Research and Applied Sciences, 17, 4, 101118, 2024.
5. Ristić, M. M. and Nadarajah, S., “A New Lifetime Distribution”, Journal of Statistical Computation and Simulation, 84, 1, 135–150, 2014.
6. Hashem, A. F. and Alyami, S. A., “Inference on a New Lifetime Distribution under Progressive Type II Censoring for a Parallel‐Series Structure”, Complexity, 1, 6684918, 2021.
7. Karakaya, K., Kınacı, İ., Kuş, C. and Akdoğan, Y., “A New Distribution with Four Parameters: Properties and Applications”, Sigma Journal of Engineering and Natural Sciences, 41, 2, 276–287, 2023.
8. Ekemezie, D. F. N. and Obulezi, O. J., “The Fav-Jerry Distribution: Another Member in the Lindley Class with Applications”, Earthline Journal of Mathematical Sciences, 14, 4, 793–816, 2024.

9. Bonferroni, C., Elmenti di Statistica Generale [Elements of General Statistics], Libreria Seber, Firenze, 1930.
10. Varadhan, R., “Numerical Optimization in R: Beyond Optim”, Journal of Statistical Software, 60, 1, 1–3, 2014.
11. Mazucheli, J., Menezes, A. F. B., Fernandes, L. B., de Oliveira, R. P. and Ghitany, M. E., “The Unit-Weibull Distribution as an Alternative to the Kumaraswamy Distribution for the Modeling of Quantiles Conditional on Covariates”, Journal of Applied Statistics, 47, 6, 954–974, 2020.
12. Mazucheli, J., Menezes, A. F. B. and Chakraborty, S., “On the One Parameter Unit-Lindley Distribution and Its Associated Regression Model for Proportion Data”, Journal of Applied Statistics, 46, 4, 700–714, 2019.
13. Krishna, A., Maya, R., Chesneau, C. and Irshad, M. R., “The Unit Teissier Distribution and Its Applications”, Mathematical and Computational Applications, 27, 1, 12, 2022.
14. Altun, E. and Cordeiro, G. M., “The Unit-Improved Second-Degree Lindley Distribution: Inference and Regression Modeling”, Computational Statistics, 35, 259–279, 2020.
15. Yousof, H. M., Alizadeh, M., Jahanshahi, S. M. A., Ghosh, T. G. R. I. and Hamedani, G. G., “The Transmuted Topp-Leone G Family of Distributions: Theory, Characterizations and Applications”, Journal of Data Science, 15, 4, 723–740, 2017.
16. Saraçoğlu, B. and Tanış, C., “A New Statistical Distribution: Cubic Rank Transmuted Kumaraswamy Distribution and Its Properties”, Journal of the National Science Foundation of Sri Lanka, 46, 4, 505–518, 2018.
17. Sağlam, Ş. and Karakaya, K., “An Alternative Bounded Distribution: Regression Model and Applications”, The Journal of Supercomputing, 80, 14, 20861–20890, 2024.