Sürekli dağılımların bir diğer odd log-logistik logaritmik sınıfı
Yıl 2018,
Cilt: 11 Sayı: 2, 55 - 72, 31.12.2018
Morad Alizadeh
Mustafa Ç. Korkmaz
,
Jehhan. A. Almamy
A. A. E. Ahmed
Öz
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.
Kaynakça
- [1] M. V. Aarset, 1987, How to identify a bathtub hazard rate, IEEE Transactions on Reliability, 36, 106-108.
- [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] 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] 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] 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] 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] G. Chen, N. Balakrishnan, 1995, A general purpose approximate goodness-of-fit test. Journal of Quality
Technology, 27, 154-161.
- [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] 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] 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] 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] 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] 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] F. Famoye, C. Lee, O. Olumolade, 2005, The beta-Weibull distribution, Journal of Statistical Theory and
Applications, 4, 121-136.
- [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] J. U. Gleaton, J. D. Lynch, 2006, Properties of generalized log-logistic families of lifetime distributions, J.
Probab. Stat. Sci. 4, 51-64.
- [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] I. S. Gradshteyn, I. M. Ryzhik, 2000, Table of Integrals, Series and Products, San Diego, Academic Press.
- [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] 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] C. Shanon, 1948, A mathematical theory of communication, Bell System Tech. J. 27, 379-423.
Another odd log-logistic logarithmic class of continuous distributions
Yıl 2018,
Cilt: 11 Sayı: 2, 55 - 72, 31.12.2018
Morad Alizadeh
Mustafa Ç. Korkmaz
,
Jehhan. A. Almamy
A. A. E. Ahmed
Öz
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.
Kaynakça
- [1] M. V. Aarset, 1987, How to identify a bathtub hazard rate, IEEE Transactions on Reliability, 36, 106-108.
- [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] 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] 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] 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] 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] G. Chen, N. Balakrishnan, 1995, A general purpose approximate goodness-of-fit test. Journal of Quality
Technology, 27, 154-161.
- [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] 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] 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] 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] 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] 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] F. Famoye, C. Lee, O. Olumolade, 2005, The beta-Weibull distribution, Journal of Statistical Theory and
Applications, 4, 121-136.
- [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] J. U. Gleaton, J. D. Lynch, 2006, Properties of generalized log-logistic families of lifetime distributions, J.
Probab. Stat. Sci. 4, 51-64.
- [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] I. S. Gradshteyn, I. M. Ryzhik, 2000, Table of Integrals, Series and Products, San Diego, Academic Press.
- [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] 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] C. Shanon, 1948, A mathematical theory of communication, Bell System Tech. J. 27, 379-423.