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Journals / İstatistikçiler Dergisi:İstatistik ve Aktüerya / 2017 / Cilt: 10 Sayı: 2

Some Theoretical and Computational Aspects of the Odd Lindley Fréchet Distribution

Oransal Lindley Fréchet Dağılımının Bazı Teorik ve Hesaplamalı Yönleri

Mustafa Ç. Korkmaz(ARTVİN ÇORUH ÜNİVERSİTESİ)0000-0003-3302-0705
Haitham M. Yousof0000-0003-4589-4944
M. Masoom Ali(Ball State University, United States of America)0000-0002-0120-9442
Pages
129–140
Publication Date
2017-12-30
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The usefulness of the odd Lindley Fréchet model is illustrated by means of three real data sets.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this article, we study an extension of the Fréchet model by using the the odd Lindley-G family of distributions, which was introduced by [17].
📊
Key Findings & Data:The Monte Carlo simulation is used for assessing the performance of the maximum likelihood method.
💡
Conclusion & Impact:The usefulness of the odd Lindley Fréchet model is illustrated by means of three real data sets.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Fréchet dağılımı · Oransal Lindley-G ailesi · Odd Lindley Fréchet dağılımı.

Abstract

In this article, we study an extension of the Fréchet model by using the the odd Lindley-G family of distributions, which was introduced by [17]. Its some statistical properties such as quantile function, density shapes, moments, generating functions and order statistics are obtained. We estimate its parameters by maximum likelihood method. The Monte Carlo simulation is used for assessing the performance of the maximum likelihood method. The usefulness of the odd Lindley Fréchet model is illustrated by means of three real data sets.

Özet

Bu çalışmada, Fréchet modelinin genişletilmiş bir versiyonu [17] tarafından önerilen oransal Lindley dağılım ailesi kullanılarak çalışılmıştır. Bu modele ait kuantil fonksiyonu, yoğunluk biçimi, momentler, üreten fonksiyon ve sıra istatistikleri gibi istatistiksel özellikleri elde edilmiştir. Model parametrelerinin en çok olabilirlik tahminleri elde edildi. En çok olabilirlik parametre tahminleri için bir simülasyon çalışılması verilmiştir. Önerilen modelin gerçek veri seti üzerindeki uygunluğu için üç veri analizi yapılmıştır.

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Cite This Article

Korkmaz, M. Ç., Yousof, H. M., Ali, M. M. (2017). Some Theoretical and Computational Aspects of the Odd Lindley Fréchet Distribution. İstatistikçiler Dergisi:İstatistik ve Aktüerya, Cilt: 10 Sayı: 2, 129–140. https://ajindex.com/articles/907268

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References (19)

  1. A.Z. Afify, G. G. Hamedani, I. Ghosh, M. E. Mead, 2015, The transmuted Marshall-Olkin Fréchet distribution: properties and applications, Int. J. Statist. Probab., 4, 132-184.
  2. A. Z. Afify, H. M. Yousof, G. M. Cordeiro, M. Ahmad, 2016a, The Kumaraswamy Marshall-Olkin Fréchet distribution with applications, Journal of ISOSS, 2, 1-18.
  3. A. Z. Afify, H. M. Yousof, G. M. Cordeiro, R. R. Pescim, G. R. Aryal, 2017, The Weibull Fréchet distribution and its applications, Journal of Applied Statistics, 43, 2608-2626.
  4. A. Z. Afify, H. M. Yousof, S. Nadarajah, 2017, The beta transmuted-H family of distributions: properties and applications, Statistics and its Inference, 10, 505-520.
  5. V. Choulakian, M.A. Stephens, 2001, Goodness-of-fit for the generalized Pareto distribution. Technometrics, 43, 478–484.
  6. G. M. Cordeiro, A. Z. Afify, H. M. Yousof, R. R. Pescim, G. R. Aryal, 2017, The exponentiated Weibull-H family of distributions: Theory and Applications, Mediterranean Journal of Mathematics, 14, 155.
  7. G. M. Cordeiro, E. M. Ortega, D. C. Cunha, 2013, The exponentiated generalized class of distributions, Journal of Data Science, 11, 1-27.
  8. M. Fréchet, 1927, Sur la loi de probabilité de lécart maximum, Ann. de la Soc. polonaisede Math, 6, 93-116.
  9. P. Feigl, M. Zelen, 1965, Estimation of exponential survival probabilities with concomitant information, Biometrics, 826-838.
  10. S. Kotz, S. Nadarajah, 2000, Extreme value distributions: Theory and applications. Imperial College Press, London.
  11. E. Krishna, K. K. Jose, T. Alice, M. M. Ristic, 2013, The Marshall-Olkin Fréchet distribution, Communications in Statistics-Theory and Methods, 42, 4091-4107.
  12. M. R. Mahmoud, R. M. Mandouh, 2013, On the transmuted Fréchet distribution, Journal of Applied Sciences Research, 9, 5553-5561.
  13. M. E. Mead, A. Z. Afify, G. G. Hamedani, I. Ghosh, 2017, The beta exponential Fréchet distribution with applications, Austrian Journal of Statistics, 46, 41-63.
  14. S. Nadarajah, A. K. Gupta, 2004,. The beta Fréchet distribution, Far East Journal of Theoretical Statistics, 14, 15-24.
  15. S. Nadarajah, S. Kotz, 2003, The exponentiated Fréchet distribution, InterStat. Available online at http://interstat.statjournals.net/YEAR/2003/abstracts/0312001.php
  16. M. D. Nichols, W. J. Padgett, 2006, A bootstrap control chart for Weibull percentiles, Quality and reliability engineering international, 22, 141-151.
  17. F G. Silva, A. Percontini, E. de Brito, M. W. Ramos, R. Venancio, G. M. Cordeiro, 2017, The odd Lindley-G family of distributions, Austrian Journal of Statistics, 46, 65-87.
  18. H. M. Yousof, A. Z. Afify, M. Alizadeh, N. S. Butt, G. G. Hamedani, M. M. Ali, 2015, The transmuted exponentiated generalized-G family of distributions, Pak. J. Stat. Oper. Res., 11, 441-464.
  19. H. M. Yousof, A. Z. Afify, A. N. Ebraheim, G. G. Hamedani, N. S. Butt, 2016, On six-parameter Fréchet distribution: properties and applications, Pak. J. Stat. Oper. Res., 12, 281-299