Topp-Leone Nadarajah Haghighi Dağılımı

Öz

Bu çalışmada yaşam verileri, güvenirlik problemleri ve yorulma ömrü çalışmalarında kullanılabilecek üç parametreli bir model üzerinde çalışılmıştır. Bu modele ait momentler, üreten fonksiyonlar, tamamlanmamış momentler ve sıra istatistikleri gibi istatistiksel ve matematiksel özellikler türetilmiştir. Tam örneklem durumuna dayalı olarak, model parametrelerinin sıradan en çok olabilirlik tahminleri elde edilmiştir. Bir simülasyon çalışması ile model parametrelerinin en çok olabilirlik tahmin edicilerinin performansları, standart sapma, yan ve hata kareler ortalamaları ile değerlendirilmiştir. Modelin kullanışlılığı, bir gerçek veri setine dayalı olarak gösterilmiştir. Önerilen dağılım bazı karşılaştırma kriterleri altında, literatürde iyi iyi bilinen birtakım dağılımlardan daha iyi uyum sağlamıştır.

Anahtar Kelimeler

• Topp-Leone dağılımı,Nadarajah-Haghighi dağılımı,en çok olabilirlik tahmini; genişletilmiş dağılımlar

Topp-Leone Nadarajah-Haghighi distribution

Öz

In this paper, a three parameter model which can be used in modeling survival data, reliability problems and fatigue life studies has been studied. We derived explicit expressions for some of its statistical and mathematical identifying properties such as ordinary moments, generating function, incomplete moments and order statistics. The maximum likelihood estimations of model parameters were also obtained -being based on complete sample. We assessed the performance of the maximum likelihood estimators in terms of standard deviations, bias and mean squared errors by means of a simulation study. The usefulness of the model was illustrated by using a real data set. The proposed distribution provides better fits than some well-known generalized distributions under the same criteria of comparison.

Anahtar Kelimeler

• Topp-Leone distribution,Nadarajah-Haghighi distribution,maximum likelihood estimation,extended distributions

Kaynakça

1. [1] I. B. Abdul-Moniem, 2016, Exponentiated Nadarajah and Haghighi exponential distribution, International Journal of Mathematical Analysis and Applications, 2, 68-73.
2. [2] A. Ahmed, H. Z. Muhammed, I. Elbatal, 2015. A new class of extension exponential distribution, International Journal of Applied Mathematical Sciences, 8, 13-30.
3. [3] M. Bourguignon, M. C. S. Lima, J. Leao, A. D. C. Nascimento, L. G. B. Pinho, G. M. Cordeiro, 2015. A new generalized gamma distribution with applications, American Journal of Mathematical and Management Sciences, 34, 309.342.
4. [4] G. M. Cordeiro, M. de Castro, 2011, A new family of generalized distributions. Journal of Statistical Computation and Simulation, 81, 883-898.
5. [5] C. R. B. Dias, 2016, New continuous distributions applied to lifetime data and survival analysis, Doctoral thesis, Universidade Federal de Pernumbuco, Recife, Brazil.
6. [6] M. A. El Damcese, D. A. Ramadan, 2015, Studies on properties and estimation problems for modified extension of exponential distribution, International Journal of Computer Applications, 125, 21-28.
7. [7] R.D. Gupta, D. Kundu, 1999, Generalized exponential distributions, Australian & New Zealand Journal of Statistics, 41, 173-188.
8. [8] A. J. Lemonte, 2013, A new exponential-type distribution with constant, decreasing, increasing, upside down bathtub and bathtub-shaped failure rate function, Computational Statistics & Data Analysis, 62, 149-170.

9. [9] A. J. Lemonte, G. M. Cordeiro, G. Moreno-Arenas, 2016, A new useful three parameter extension of the exponential distribution, Statistics, 50, 312.337.
10. [10] E. T. Lee, J. W. Wang, 2003, Statistical Methods for Survival Data Analysis, Third ed. Wiley, New York.
11. [11] S. Nadarajah, F. Haghighi, 2011. An extension of the exponential distribution, Statistics, 45, 543-558.
12. [12] S. Nadarajah, S. Kotz, 2006, The beta exponential distribution, Reliability engineering & System Safety, 91, 689-697.
13. [13] E. M. M Ortega, A. J. Lemonte, G. O. Silva, G. M. Cordeiro, 2015, New flexible models generated by gamma random variables for lifetime modelling, Journal of Applied Statistics, 42, 2159-2179.
14. [14] Y. Sangsanit, W. Bodhisuwan, 2016, The Topp-Leone generator of distributions: Properties and inferences, Songklanakarin J. Sci. Technol., 38, 537-548.
15. [15] V. T. Vedo, A. D. C. Nascimento, W.R. Miranda Filho, M. C. S. Lima, L. G. B. Pinho, G. M. Cordeiro, 2016, Some computational and theoretical aspects of the exponentiated generalized Nadarajah-Haghighi distribution. Chilean Journal of Statistics, Forthcoming, in https://arxiv.org/pdf/1610.08876.pdf.
16. [16] O. M. Yazar, 2015, An extension of the exponential distribution via Kumaraswamy-G family, Master’s thesis, Recep Tayyip Erdoğan University, Rize, Turkey