Maximum Likelihood Estimation for Parameters of Extended Burr XII Distribution and Bias Correction Based on K-Records

محورهای موضوعی : مجله بین المللی ریاضیات صنعتی

M. Rajaei Salmasi ¹ (Department of Mathematics, Urmia Branch, Islamic Azad University, Urmia, Iran.)

تاریخ دریافت : 1400/08/22 تاریخ پذیرش : 1400/08/22 تاریخ انتشار : 1400/10/11

کلید واژه: MLE, Bias corrected estimator, K-Records, Extended Burr XII distribution,

چکیده مقاله :

Our aim at this paper is to estimate the parameters of extended Burr XII (EBXII) based on krecords with corrected bias. To get this goal maximum likelihood estimator (MLE) is applied and bias correction for ML estimation is considered to get better and improved estimator. Numerical results for comparison of performances of estimators are also presented.

چکیده انگلیسی:

هدف ما در این مقاله برآورد پارامترهای توزیع بر 12 مبسوط بر پایه ی مقادیر رکورد k و تصحیح اریبی آن است. برای نیل به این هدف با استفاده از بیشینه راستنمایی برآوردی بدست آمده و سپس با تصحیح اریبی آن برآوردگری بهبود یافته ایجاد شده است. برای مقایسه و بررسی عملکرد برآوردگرها از روش های عددی استفاد شده است.

منابع و مأخذ:

[1] J. Ahmadi, Record values, theory and applications, Mashhad, Iran: Ferdowsi University of Mashhad. Ph. D Thesis, 2000.
[2] M. Ahsanullah, V. B. Nevzorov, Records via Probability Theory, Atlantis Press, 2015.
[3] C. Barry Arnold, N. Balakrishnan, H. N. Nagaraja, Records, John Wiley & Sons, 1998.
[4] M. S. Bartlett, Approximate Confidence Intervals, Biometrika 40 (1953) 12-19.
[5] K. N. Chandler, The distribution and frequency of record values, Journal of the Royal Statistical Society: Series B (Methodological) 14 (1952) 220-228.
[6] M. Gauss, Cordeiro and Francisco CribariNeto, An Introduction to Bartlett Correction and Bias Reduction, Springer-Verlag Berlin Heidelberg, 2014.
[7] M. Gauss, Cordeiro and Ruben Klein, Bias correction in arma models, Statistics & Probability Letters 19 (1994) 169-176.
[8] D. R. Cox, E. J. Snell, A general definition of residuals, Journal of the Royal Statistical Society. Series B (Methodological) 30 (1968) 248-275.
[9] Q. Shao, Notes on maximum likelihood estimation for the three-parameter burrxii distribution, Computational Statistics and Data Analysis 45 (2004) 675-687.
[10] Q. Shao, H. Wong, J. Xia, Wai-Cheung Ip, Models for extremes using the extended three-parameter burr xii system with application to flood frequency analysis / modles dextrmes utilisant le systme burr xii tendu trois paramtres et application lanalyse frquentielle des crues, Hydrological Sciences Journal 49 (2004) 685-702.
[11] I. Usta, Different estimation methods for the parameters of the extended burrxii distribution, Journal of Applied Statistics 40 (2013) 397-414.
[12] B. Kopociski, W. Dziubdziela, Limiting properties of the k-th record values, Applicationes Mathematicae 15 (1976) 187-190.
[13] J. Alan Watkins, An algorithm for maximum likelihood estimation in the three parameter burrxii distribution, Computational Statistics and Data Analysis 32 (1999) 19-27.