Turkiye Klinikleri Journal of Biostatistics

.: ORIGINAL RESEARCH
A Study on Topp-Leone Kumaraswamy Fréchet Distribution with Applications: Methodological Study
Uygulamalarla Topp-Leone Kumaraswamy Fréchet Dağılımı Üzerine Bir Araştırma: Metodolojik Çalışma
Sule Omeiza BASHIRUa
aDepartment of Mathematics and Statistics, Confluence University of Science and Technology, Osara, Kogi State, Nigeria
Turkiye Klinikleri J Biostat. 2024;16(1):1-15
doi: 10.5336/biostatic.2023-99766
Article Language: EN
Full Text
ABSTRACT
 Objective: The aim of this study is to introduce and analyze the Topp-Leone Kumaraswamy Fréchet (TLKFr) distribution a new probability distribution model. This model extends the classical Fréchet distribution by introducing three additional positive shape parameters to enhance flexibility and robustness. Material and Methods: The novel distribution is based on the ToppLeone Kumaraswamy generalized distribution family, incorporating three shape parameters. This foundation allows for the derivation of both the cumulative distribution function and probability density function for the new distribution. The study also extensively explores the mathematical properties of this distribution, including the survival, hazard, and quantile functions. Parameter estimation is conducted using the maximum likelihood estimation (MLE) technique. Results: The study introduces the TLKFr distribution, providing mathematical expressions for key statistical measures. Parameters were estimated using MLE technique. Plots illustrate the distribution's characteristics, showing positive skewness and reliable survival analysis predictions. Simulation analysis indicates decreasing bias and root mean square error (RMSE) with larger sample sizes, emphasizing reliability. Application to two real-life datasets, demonstrates the TLKFr distribution consistently outperforming rival models, supported by goodness-of-fit statistics. Conclusion: The study introduces and analyzes the TLKFr distribution, enhancing the traditional Fréchet distribution with three additional shape parameters. Mathematical characteristics are explored, employing MLE for parameter estimation. A simulation study underscores the distribution's strong reliability, evident in decreasing bias and RMSE with increasing sample size. When tested with real datasets, the TLKFr distribution outperforms alternative models, highlighting its significance in representing real-world phenomena and validating its applicability to the two datasets examined in this study.

Keywords: Maximum likelihood estimation; COVID-19; goodness of fit; Frechet distribution; order statistic
ÖZET
 Amaç: Bu çalışmanın amacı, yeni bir olasılık dağılım modeli olan Topp-Leone Kumaraswamy Fréchet (TLKFr) dağılımını tanıtmak ve analiz etmektir. Bu model, esnekliği ve sağlamlığı artırmak için üç ek pozitif şekil parametresi uygulayarak klasik Fréchet dağılımını genişletir. Gereç ve Yöntemler: Yeni dağılım, üç şekil parametresini içeren Topp-Leone Kumaraswamy genelleştirilmiş dağılım ailesine dayanmaktadır. Bu temel yeni dağılım için hem kümülatif dağılım fonksiyonunun hem de olasılık yoğunluk fonksiyonunun türetilmesine olanak sağlar. Çalışma aynı zamanda sağkalım, tehlike ve niceliksel işlevler de dâhil olmak üzere bu dağılımın matematiksel özelliklerini de kapsamlı bir şekilde araştırmaktadır. Parametre tahmini, maksimum olabilirlik tahmini [the maximum likelihood estimation (MLE)] tekniği kullanılarak gerçekleştirilir. Bulgular: Çalışma, temel istatistiksel ölçümler için matematiksel ifadeler sağlayan TLKFr dağılımını tanıtmaktadır. Parametreler, MLE tekniğinin kullanılmasıyla tahmin edilmiştir. Grafikler, pozitif çarpıklığı ve güvenilir sağkalım analizi tahminlerini gösteren dağılımın özelliklerini göstermektedir. Simülasyon analizi, daha büyük örneklem boyutlarıyla azalan sapma ve kök ortalama kare hatasına [root mean square error (RMSE)] işaret ederek güvenilirliği vurgulamaktadır. Gerçek hayattan iki veri setine yapılan uygulama, TLKFr dağılımının uyum iyiliği istatistikleriyle desteklenen rakip modellerden sürekli olarak daha iyi performans gösterdiğini ortaya koymaktadır. Sonuç: Bu çalışma, geleneksel Fréchet dağılımını üç ek şekil parametresi ile geliştiren TLKFr dağılımını tanıtmakta ve analiz etmektedir. Parametre tahmini için MLE kullanılarak matematiksel özellikler araştırılmıştır. Bir simülasyon çalışması, artan örneklem büyüklüğü ile azalan sapma ve RMSE ile dağılımın güçlü güvenilirliğinin altını çizmektedir. TLKFr dağılımı, gerçek veri kümeleriyle test edildiğinde alternatif modellerden daha iyi performans göstererek gerçek dünya olaylarını temsil etmedeki önemini vurgulamakta ve bu çalışmada incelenen iki veri kümesine uygulanabilirliğini doğrulamaktadır.

Anahtar Kelimeler: Maksimum olabilirlik tahmini; COVID-19; uyumun iyiliği; Fréchet dağılımı; sıra istatistiği
REFERENCES:
  1. Fréchet M. Sur la loi des erreurs dIobservation. Bulletin de la Société Mathématique de Moscou. 1924;33:5-8. [Link] 
  2. Kotz S, Nadarajah S. Extreme Value Distributions: Theory and Applications. 1st ed. London: Imperial College Press; 2000. [Crossref] 
  3. Mubarak M. Parameter estimation based on the Fréchet progressive type II censored data with binomial removals. Journal of Quality, Statistics and Reliability. 2012:1-5. [Crossref] 
  4. Nadarajah S, Gupta AK. The beta Fréchet distribution. Far East Journal of Theoretical Statistics. 2004;1(4):15-24. [Link] 
  5. Nadarajah S, Kotz S. The exponentiated Fréchet distribution. Interstat Electronic Journal. 2003:1-7. [Link] 
  6. Mahmoud MR, Mandouh RM. On the transmuted Fréchet distribution. Journal of Applied Sciences Research. 2013;9(10):5553-61. [Link] 
  7. Krishna E, Jose KK, Alice T, Ristic MM. The Marshall-Olkin Fréchet distribution. Communications in Statistics-Theory and Methods. 2013;42:4091-107. [Crossref] 
  8. da Silva RV, de Andrade TA, Maciel DBM, Campos RPS, Cordeiro GM. A new lifetime model: the gamma extended Fréchet distribution. Journal of Statistical Theory and Applications. 2013;12:39-54. [Crossref] 
  9. Mead ME, Abd-Eltawab AR. A note on Kumaraswamy Fréchet distribution. Australian Journal of Basic and Applied Sciences. 2014;8(15):294-300. [Link] 
  10. Afify AZ, Hamedani GG, Ghosh I, Mead ME. The transmuted Marshall-Olkin Fréchet distribution: properties and applications. International Journal of Statistics and Probability. 2015;4(4):132-48. [Crossref] 
  11. Afify AZ, Yousof HM, Cordeiro GM, Ortega EMM, Nofal ZM. The Weibull Fréchet distribution and its applications. Journal of Applied Statistics. 2016;43(14):2608-26. [Crossref] 
  12. Mead ME, Afify AZ, Hamedani GG, Ghosh I. The beta exponential Fréchet distribution with applications. Austrian Journal of Statistics. 2017;46(1):41-63. [Crossref] 
  13. Ramos PL, Nascimento D, Louzada F. The long term fréchet distribution: estimation, properties and its application. Biom Biostat Int J. 2017;6(3):357-62. [Crossref] 
  14. Tablada CJ, Cordeiro GM. The modified Fréchet distribution and its properties. Communications in Statistics-Theory and Methods. 2017;46(21):10617-39. [Crossref] 
  15. Mansour MM, Abd Elrazik EM, Altun E, Afify AZ, Iqbal Z. A new three-parameter Fréchet distribution: properties and applications. Pak J Statist. 2018;34(6):441-58. [Link] 
  16. Mansour MM, Aryal G, Afify AZ, Ahmad M. The kumaraswamy exponentiated Fréchet distribution. Pak J Statist. 2018;34(3):177-93. [Link] 
  17. Abouelmagd THM, Hamed MS, Afify AZ, Al-Mofleh H, Iqbal Z. The Burr X Fréchet distribution with its properties and applications. Journal of Applied Probability and Statistics. 2018;13(1):23-51. [Link] 
  18. Ramos PL, Louzada F, Ramos E, Dey S. The Fréchet distribution: estimation and application-an overview. Journal of Statistics and Management Systems. 2019:1-24. [Link] 
  19. Hamed MS, Aldossary F, Afify AZ. The four-parameter Fréchet distribution: properties and applications. Pakistan Journal of Statistics and Operation Research. 2020;16(2):249-64. [Crossref] 
  20. Ibrahim S, Doguwa SI, Audu I, Jibril HM. The Topp leone kumaraswamy-g family of distributions with applications to cancer disease data. Journal of Biostatistics and Epidemiology. 2020;6(1):37-48. [Link] 
  21. Sule BO, Halid OY. On gompertz exponentiated inverse rayleigh distribution. Reliability: Theory & Applications. 2023;18(1):412-24. [Link] 
  22. Sule OB. A new extended generalized inverse exponential distribution: properties and applications. Asian Journal of Probability and Statistics. 2021;11(2):30-46. [Crossref] 
  23. Isa AM, Sule OB, Alhaji AB, Adepoju AA, Itopa II. Sine-exponential distribution: its mathematical properties and application to real datasets. UMYU Scientifica, 2022;1(1):127-31. [Crossref] 
  24. Halid OY, Sule OB. A classical and bayesian estimation techniques for gompertz inverse rayleigh distribution: properties and applications. Pakistan Journal of Statistics. 2022;38(1):49-76. [Link] 
  25. Trayer VN. Inverse Rayleigh (IR) model. Proceedings of the Academy of Science. Belarus: USSR; 1964. [Link] 
  26. Al-Marzouki S, Jamal F, Chesneau C, Elgarhy M. Topp-leone odd frechet generated family of distributions with applications to COVID-19. Data Sets, Computer Modeling in Engineering and Sciences. 2020;125(1):437-58. [Crossref] 
  27. Andrews DF, Herzberg AM. Data: A Collection of Problems from Many Fields for the Student and Research Worker. New York: Springer Series in Statistics; 1985.
  28. Barlow RE, Toland RH, Freeman T. A Bayesian analysis of stress rupture life of Kevlar 49/epoxy spherical pressure vessels. Procedings Conference on Applications of Statistics. New York: Marcel Dekker; 1984.

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