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http://dx.doi.org/10.5351/CKSS.2007.14.2.389

Bayesian Estimation of the Reliability Function of the Burr Type XII Model under Asymmetric Loss Function  

Kim, Chan-Soo (Department of Applied Statistics, Kongju National University)
Publication Information
Communications for Statistical Applications and Methods / v.14, no.2, 2007 , pp. 389-399 More about this Journal
Abstract
In this paper, Bayes estimates for the parameters k, c and reliability function of the Burr type XII model based on a type II censored samples under asymmetric loss functions viz., LINEX and SQUAREX loss functions are obtained. An approximation based on the Laplace approximation method (Tierney and Kadane, 1986) is used for obtaining the Bayes estimators of the parameters and reliability function. In order to compare the Bayes estimators under squared error loss, LINEX and SQUAREX loss functions respectively and the maximum likelihood estimator of the parameters and reliability function, Monte Carlo simulations are used.
Keywords
Burr type XII distribution; Laplace approximation; LINEX loss function; SQUAREX loss function;
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1 Varian, H. (1975). A Bayesian approach to real estate assessment, (Fienberg S. E. and Zellner A., eds.), Studies in Bayesian Econometrics and Statistics in honour of Leonard J. Savage, North-Holland, Amsterdam, 195-208
2 Wingo, D. R. (1983). Maximum likelihood methods for fitting the Burr type XII distribution to life test data. Biometrical Journal, 25, 1099-1113
3 Zellner, A. (1986). Bayesian estimation and prediction using asymmetric loss function. Journal of the American Statistical Association, 81, 446-451   DOI
4 AI-Hussaini, E. K. and Jaheen, Z. F. (1992). Bayesian esimation of the parameters, reliability and failure rate functions of the Burr Type XII failure model. Journal of Statistical Computation and Simulation, 41, 31-40   DOI
5 AI-Hussaini, E. K. and Jaheen, Z. F. (1994). Approximate Bayes estimators applied to the Burr model. Communications in Statistics-Theory and Methods, 23, 99-121   DOI   ScienceOn
6 Burr, I. W. (1942). Cumulative frequency functions. Annals of Mathematical Statistics, 13, 215-222   DOI
7 Chaturvedi, A., Bhatti, M. I. and Kumar, K. (2000). Bayesian analysis of disturbances variance in the linear regression model under asymmetric loss functions. Applied Mathematics and Computation, 114, 149-153   DOI   ScienceOn
8 Dubey, S. D. (1972). Statistical contributions to reliability engineering. ARL TR 72-0120, AD 774537
9 Dubey, S. D. (1973). Statistical treatment of certain life testing and reliability problems. ARL TR 73-0155, AD 774537
10 Lindely, D. V. (1980). Approximate Bayesian methods. Trabajos de Stadistca, 21, 223-237
11 Tierney, L. and Kadane, J. B. (1986). Accurate approximations for posterior moments and marginal densities. Journal of the American Statistical Association, 81, 82-86   DOI
12 Ali Mousa, M. A. and Jaheen, Z. F. (2002). Statistical inference for the Burr model based on progressively censored data. Computers & Mathematics with Applications, 43, 1441-1449   DOI   ScienceOn
13 Moore, D. and Papadopoulos, A. S. (2000). The Burr type XII distribution as a failure model under various loss functions. Microelectronics Reliability, 40, 2117-2122   DOI   ScienceOn
14 Papadopoulos, A. S. (1978). The Burr distribution as a failure model from a Bayesian approach. IEEE Transactions on Reliability, 27, 369-371   DOI
15 Thompson, R. D. and Basu, A. P. (1996). Asymmetric Loss Function for Estimating System Reliability. (Berry D. A., Chaloner K. M., Geweke J. K., eds.), Bayesian Analysis in Statistics and Econometrics, John Wiley & Sons, New York