برآوردهای E-بیز و بیزی سلسله مراتبی پارامتر اسکالر توزیع وایبول بر اساس نمونه های سانسور فزآینده نوع دوم با سه تابع زیان

نوع مقاله: علمی- پژوهشی

نویسنده

عضو هیات علمی دانشگاه پیام نور مرکز صومعه سرا

چکیده

در این مقاله برآوردهای E-بیز و بیزی سلسله مراتبی پارامتر اسکالر توزیع وایبول دو پارامتری بر اساس نمونه‌های سانسور فزآینده نوع دوم و تحت توابع زیان درجه دوم، آنتروپی و لاینکس به دست آورده شده و سپس با استفاده از شبیه‌سازی مونت کارلو و به کمک معیارهای قدر مطلق اریبی و میانگین مربع خطای برآوردگرها، این برآوردگرها با هم و با برآوردگر بیز مقایسه می‌شوند.

کلیدواژه‌ها


References

 

Balakrishnan, N. and Cohen, A.C. (1991). Order Statistics and Inference: Estimation Methods.Academic Press, San Diego.

Balakrishnan, N. and Sandhu, R.A.A (1995). Simple simulational algorithm for generating progressive Type-II censored samples. The Amer. Statist. 49, 229-230.

Balakrishnan, N. and Aggarwala, R. (2000). Progressive Censoring: Theory, Methods and Applications. Birkh auser, Boston - 215.

Balakrishnan, N. and Asgharzadeh, A. (2005). Inference for the scaled halflogistic distribution based on progressively Type II censored samples. Commun. Statist. Theory Meth. 34, 73- 87.

Berger, J. O. (1985). Statistical Decision Theory and Bayesian Analysis, second ed., Springer-Verlag, New York.

Balakrishnan, N and Katen, M. (2008). On the maximum likelihood estimation of parameters of Weibull distribution based on complete and censored data, Statistics and Probability Letters, 78(17), 2971- 2975.

Cho, Y., Sun, H. and Lee, K. (2015), Estimating the Entropy of a Weibull Distribution under Generalized Progressive Hybrid Censoring, Entropy, 17, 102-122.

Canavos, G.C. and Taokas, C. (1973). Bayesian Estimation of Life Parameters in the Weibull Distribution, Operations Research, 755-763.

Guure, C.B., Ibrahimi, N.A. and Mohammed Ahmed, A.O. (2012). Bayesian Estimation of Two-Parameter Weibull Distribution Using Extension of Jeffreys’ Prior Information with Three Loss Functions, Mathematical Problems in Engineering, doi: 10.1155/-2012/589640.

Han, G.J. and Shapiro, S.S. (1967). Statistical Models in Enginearing, John, Wiley and Sons.

Han, M. (1997). The structure of hierarchical prior distribution and its applications, Chinese Operations Research and Management Science, 6(3), 31-40.

Han, M. (2009). E-Bayesian estimation and hierarchical Bayesian estimation of failure rate, Applied Mathematical Modelling, 33(4), 1915-1922.

Han, M. (2011). E-Bayesian estimation of the reliability derived from Binomial distribution, Applied Mathematical Modelling, 35, 2419-2424.

Johnson, N.L., Kotz, S. and Balakrishnan, N. (1995). Continuous Univariate Distributions, Vol. 2, 2nd ed., John Wiley and Sons.

Jaheen, Z.F. and Okasha, H.M. (2011). E- Bayesian estimation for the Burr type XII model based on type-2 censoring, Applied Mathematical Modelling, 35, 4730-4737.

Lindley, D.V. and Smith, A.F. (1972). Bayes estimation for the linear model, Journal of the Royal Statistical Society-Series B, 34, 1–41.

Reyad, H., Younis, A. M. and Alkhedir, A. (2016). Comparison of estimates using censored samples from Gompertz model: Bayesian, E-Bayesian, hierarchical Bayesian and empirical Bayesian schemes, International Journal of Advanced Statistics and Probability, 4(1), 47-61.

Reyad, H., Younis, A. M. and Alkhedir, A. (2016). Quasi-E-Bayesian criteria versus quasi-Bayesian, quasi-hierarchical Bayesian and quasi-empirical Bayesian methods for estimating the scale parameter of the Erlang distribution, International Journal of Advanced Statistics and Probability, 4(1), 62-74.

Reyad, H., Younis, A. M. and Ahmad, O. (2016). Quasi-E-Bayesian Estimation of the Frechet Model, British Journal of Mathematics and Computer Science, 4(1), 62-74.

Wang, J.; Li, D. and Chen, D. (2012). E-Bayesian Estimation and Hierarchical Bayesian Estimation of the System Reliability Parameter, Systems Engineering Procedia, 3, 282 – 289.