Sürekli dağılımların bir diğer odd log-logistik logaritmik sınıfı

Abstract

Bu çalışmada, sürekli dağılımların yeni bir sınıfı sunulmuştur ve bu yeni dağılım sınıfının matematiksel özellikleri çalışılmıştır. Model parametreleri en çok olabilirlik tahmin yöntemi ile elde edilmiş ve bu tahmin edicilerin performansları yan ve hata kareler ortalamasına dayalı olarak bir simülasyon çalışması üzerinde gözlemlenmiştir. Gerçek bir seti için, yeni sınıfın özel bir üyesi diğer iyi bilinen dağılım sınıflarının üyelerinden daha iyi uyum sağlamıştır.

Keywords

• Odd log-logistik ailesi,En çok olabilirlik tahmini,Birleştirilmiş sınıf,Sıra istatistikleri

Another odd log-logistic logarithmic class of continuous distributions

Abstract

In this work, a new class of continuous distributions is presented and the mathematical properties of the new distribution class is studied. We estimate the model parameters by the maximum likelihood method and assess its performance based on biases and mean squared errors in a simulation study framework. For the real data set, the special member of the new class provides a better fit than other models generated by other well-known families.

Keywords

• Odd Log-Logistic Family,Maximum Likelihood Estimation,Compound Class,Order Statistics

References

1. [1] M. V. Aarset, 1987, How to identify a bathtub hazard rate, IEEE Transactions on Reliability, 36, 106-108.
2. [2] D. F. Andrews, A. M. Herzberg, 1985, Data: A Collection of Problems from Many Fields for the Student and Research Worker, Springer Series in Statistics, New York.
3. [3] M. Alizadeh, M. Emadi, M. Doostparast, M. G. M. Cordeiro, E.M.M. Ortega, R. R. Pescim, 2015. Kumaraswamy odd log-logistic family of distributions: Properties and applications. Hacettepe Journal of Mathematics and Statistics, 44, 1491-1512.
4. [4] M. Alizadeh, F. Lak, M. Rasekhi, T. G. Ramires, H. M. Yousof, E. Altun, 2017, The odd log-logistic Topp Leone G family of distributions: heteroscedastic regression models and applications. Computational Statistics, 33, 1217-1244.
5. [5] M. Alizadeh, H.M. Yousof, M. Rasekhi, E. Altun, E. 2018, The odd log-logistic Poisson-G Family of distributions, Journal of Mathematical Extensions, 12-1.
6. [6] E. Brito, G.M. Cordeiro, H. M. Yousof, M. Alizadeh, G. O. Silva, 2017, Topp-Leone odd log -logistic family of distributions, Journal of Statistical Computation and Simulation, 87, 3040- 3058.
7. [7] G. Chen, N. Balakrishnan, 1995, A general purpose approximate goodness-of-fit test. Journal of Quality Technology, 27, 154-161.
8. [8] K. Cooray, M. M. Ananda, 2008, A generalization of the half-normal distribution with applications to lifetime data, Communications in Statistics-Theory and Methods, 37, 1323-1337.

9. [9] G.M. Cordeiro, M. Alizadeh, E. M. M. Ortega, L. H. V. Serrano, 2016a, The Zografos Balakrishnan odd log-logistic family of distributions: Properties and Applications. Hacet. J. Math. Stat, 45, 1781-1803.
10. [10] G. M. Cordeiro, M. Alizadeh, G. Ozel, B. Hosseini, B. E. M. M. Ortega, E. Altun, 2017, The generalized odd log-logistic family of distributions: properties, regression models and applications. Journal of Statistical Computation and Simulation, 87, 908-932.
11. [11] G. M. Cordeiro, M. Alizadeh, M. H. Tahir, M. Mansoor, M. Bourguignon, G. G. Hamedani, (2016b). The beta odd log-logistic generalized family of distributions, Hacettepe Journal of Mathematics and Statistics, 45, 1175-1202.
12. [12] J. N. D. Cruz, E. M. M. Ortega, G.M. Cordeiro, 2016, The log-odd log-logistic Weibull regression model: modelling, estimation, influence diagnostics and residual analysis. Journal of Statistical Computation and Simulation, 86, 1516-1538.
13. [13] D. L. Evans, J. H. Drew, L. M. Leemis, 2008, The distribution of the Kolmogorov-Smirnov, Cramer-von Mises, and Anderson-Darling test statistics for exponential populations with estimated parameters, Communications in Statistics-Simulation and Computation, 37, 1396-1421.
14. [14] F. Famoye, C. Lee, O. Olumolade, 2005, The beta-Weibull distribution, Journal of Statistical Theory and Applications, 4, 121-136.
15. [15] J. U. Gleaton, J. D. Lynch, 2004, On the distribution of the breaking strain of a bundle of brittle elastic fibers, Adv. Appl. Probab. 36, 98-115.
16. [16] J. U. Gleaton, J. D. Lynch, 2006, Properties of generalized log-logistic families of lifetime distributions, J. Probab. Stat. Sci. 4, 51-64.
17. [17] J. U. Gleaton, J. D. Lynch, 2010, Extended generalized log-logistic families of lifetime distributions with an application. J. Probab. Stat. Sci. 8, 1-17.
18. [18] I. S. Gradshteyn, I. M. Ryzhik, 2000, Table of Integrals, Series and Products, San Diego, Academic Press.
19. [19] M. Ç. Korkmaz, H. M. Yousof, G. G. Hamedani, 2018, The exponential Lindley odd log-logistic G family: properties, characterizations and applications. Journal of Statistical Theory and Applications, 17, 554-571.
20. [20] A. Renyi, 1961, On measures of entropy and information. - In: Neymann, J. (ed.), Proc. 4th Berkeley Symp. Math. Statist. Probabil. (Vol. 1). Univ. of California Press, 547-561.
21. [21] C. Shanon, 1948, A mathematical theory of communication, Bell System Tech. J. 27, 379-423.