Abstract
Bu makalede, log-Dagum dağılımı
için yaklaşık Bayes tahmini problemi düşünüldü. İlk olarak, Log-Dagum dağılımının
bilinmeyen parametreleri için en çok olabilirlik tahmin edicileri ve bu tahmin
edicilere dayalı asimptotik güven aralıkları oluşturuldu. Ayrıca, bu dağılımın
bilinmeyen parametreleri için karesel kayıp fonksiyonu altında yaklaşık Bayes
tahmin edicileri Tierney and Kadane yaklaşımı kullanılarak elde edildi. Bu
tahmin edicilerin performanslarını, hata kareler ortalaması ve yan bakımından
karşılaştırmak için bir Monte-Carlo simülasyon çalışması gerçekleştirilmiştir.
Son olarak bu dağılım için gerçek veri analizi gerçekleştirilmiştir.
Keywords
Log-Dagum dağılımı En çok olabilirlik tahmini Asimptotik güven aralığı Yaklaşık Bayes tahmini Tierney and Kadane yaklaşımı
References
- Dagum, Camilo. New model of personal income-distribution-specification and estimation. Economie appliquée. 30-3 (1977) 413-437.
- Dagum, C. The Generation and Distribution of Income, the Lorenz Curve and the Gini Ratio, Economie Appliqu ée. 33, (1980) 327-367.
- Domma, F., Asimmetrie Puntuali e Trasformazioni Monotone. Quaderni di Statistica. 3 (2001) 145-164.
- Domma, F., Kurtosis diagram for the Log-Dagum distribution. Statistica Applicazioni. 2 (2004) 3–23.
- Domma, F., Perri, P. F., Some developments on the log-Dagum distribution. Statistical Methods and Applications, 18-2 (2009) 205-220.
- Tierney, L., Kadane, J. B., Accurate approximations for posterior moments and marginal densities. Journal of the american statistical association, 81(393) (1986) 82-86.
- Gencer, G., and Saracoglu, B. Comparison of approximate Bayes Estimators under different loss functions for parameters of Odd Weibull Distribution. Journal of Selcuk University Natural and Applied Science, 5-1 (2016) 18-32.
- Howloader, H.A., Hossain, A. M., Bayesian survival estimation of Pareto distribution of second kind based on failure-censored data, Computational Statistics and Data Analysis, 38 (2002) 301-314.
- Mousa, M. A., Jaheen, Z. F., Statistical inference for the Burr model based on progressively censored data. Computers and Mathematics with Applications, 43-10 (2002) 1441-1449.
- Kınacı, İ., Karakaya, K., Akdoğan, Y., Kuş, C., Kesikli Chen Dağılımı için Bayes Tahmini. Selçuk Üniversitesi Fen Fakültesi Fen Dergisi, 42-2 (2016) 144-148.
- Tanış, C., Saraçoğlu, B., Statistical Inference Based on Upper Record Values for the Transmuted Weibull Distribution. International Journal of Mathematics and Statistics Invention (IJMSI), 5-9 (2017) 18-23.
- Kharazmi, O., Saadatinik, A., Hyperbolic cosine-f family of distributions with an application to exponential distribution. Gazi University Journal of Science, 29-4 (2016) 811-829.
- Andrews, D. F., and A. M. Herzberg, Prognostic variables for survival in a randomized comparison of treatments for prostatic cancer. Data (1985) 261-274.
- Barlow, R. E., Toland, R. H., and Freeman, T., A Bayes Analysis of Stress-Rupture Life of Kevlar/Eproxy Spherical Pressure Vessels, in Proceedings of the Canadian Conference in Applied Statistics, New York: Marcel Dekker (1984).
- Merovci, F., Alizadeh, M., Hamedani, G. G., Another generalized transmuted family of distributions: properties and applications. Austrian Journal of Statistics, 45 (2016) 71-93.
Abstract
In this article, the approximate Bayes estimation
problem for the log-Dagum distribution with three parameters is considered.
Firstly, the maximum likelihood estimators and asymptotic confidence intervals
based on these estimators for unknown parameters of log-Dagum distribution are
constructed. In addition, approximate
Bayes estimators under squared error loss function for unknown parameters of
this distribution are obtained using Tierney and Kadane approximation. A
Monte-Carlo simulation study is performed to compare performances of maximum
likelihood and approximate Bayes estimators in terms of mean square errrors and
biases. Finally, real data analysis for this distribution is performed.
Keywords
Log-Dagum Distribution Maximum Likelihood Estimation Asymptotic Confidence Interval Approximate Bayesian Estimation Tierney-Kadane Approximation
References
- Dagum, Camilo. New model of personal income-distribution-specification and estimation. Economie appliquée. 30-3 (1977) 413-437.
- Dagum, C. The Generation and Distribution of Income, the Lorenz Curve and the Gini Ratio, Economie Appliqu ée. 33, (1980) 327-367.
- Domma, F., Asimmetrie Puntuali e Trasformazioni Monotone. Quaderni di Statistica. 3 (2001) 145-164.
- Domma, F., Kurtosis diagram for the Log-Dagum distribution. Statistica Applicazioni. 2 (2004) 3–23.
- Domma, F., Perri, P. F., Some developments on the log-Dagum distribution. Statistical Methods and Applications, 18-2 (2009) 205-220.
- Tierney, L., Kadane, J. B., Accurate approximations for posterior moments and marginal densities. Journal of the american statistical association, 81(393) (1986) 82-86.
- Gencer, G., and Saracoglu, B. Comparison of approximate Bayes Estimators under different loss functions for parameters of Odd Weibull Distribution. Journal of Selcuk University Natural and Applied Science, 5-1 (2016) 18-32.
- Howloader, H.A., Hossain, A. M., Bayesian survival estimation of Pareto distribution of second kind based on failure-censored data, Computational Statistics and Data Analysis, 38 (2002) 301-314.
- Mousa, M. A., Jaheen, Z. F., Statistical inference for the Burr model based on progressively censored data. Computers and Mathematics with Applications, 43-10 (2002) 1441-1449.
- Kınacı, İ., Karakaya, K., Akdoğan, Y., Kuş, C., Kesikli Chen Dağılımı için Bayes Tahmini. Selçuk Üniversitesi Fen Fakültesi Fen Dergisi, 42-2 (2016) 144-148.
- Tanış, C., Saraçoğlu, B., Statistical Inference Based on Upper Record Values for the Transmuted Weibull Distribution. International Journal of Mathematics and Statistics Invention (IJMSI), 5-9 (2017) 18-23.
- Kharazmi, O., Saadatinik, A., Hyperbolic cosine-f family of distributions with an application to exponential distribution. Gazi University Journal of Science, 29-4 (2016) 811-829.
- Andrews, D. F., and A. M. Herzberg, Prognostic variables for survival in a randomized comparison of treatments for prostatic cancer. Data (1985) 261-274.
- Barlow, R. E., Toland, R. H., and Freeman, T., A Bayes Analysis of Stress-Rupture Life of Kevlar/Eproxy Spherical Pressure Vessels, in Proceedings of the Canadian Conference in Applied Statistics, New York: Marcel Dekker (1984).
- Merovci, F., Alizadeh, M., Hamedani, G. G., Another generalized transmuted family of distributions: properties and applications. Austrian Journal of Statistics, 45 (2016) 71-93.
Details
| Primary Language | English |
|---|---|
| Journal Section | Natural Sciences |
| Authors | |
| Publication Date | June 30, 2019 |
| Submission Date | November 18, 2018 |
| Acceptance Date | January 14, 2019 |
| Published in Issue | Year 2019 |