Non-parametric empirical Bayes procedure

Reliability Engineering and System Safety

Volumn 80, Issue 2, 2003, Pages 115-122

  Sarhan, Ammar ^a,b  

^a KING SAUD UNIVERSITY   (Saudi Arabia)

^b Mansoura University   (Egypt)

Author keywords

Bayes procedure; Density function; Posterior risk

Indexed keywords

FAILURE ANALYSIS; PROBABILITY; RISK ASSESSMENT; WEIBULL DISTRIBUTION;

BAYES PROCEDURE;

PARAMETER ESTIMATION;

EID: 0037401611     PISSN: 09518320     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0951-8320(03)00003-6     Document Type: Article

References (29)

1. Bendel R.B., Carlin B.P. Bayes methods in the ecological fallacy context: estimation of individual correlation from aggregate data. Commun Stat Theory Meth. 19:1990;2595-2623.
2. Bennett G.K., Martz H.F. A continuous empirical Bayes smoothing technique. Biometrika. 59:1972;361-368.
3. Ciesielski Z. Nonparametric polynomial density estimation. Probab Math Stat. 9:1988;1-10.
4. Clemmer B.A., Krutchkoff R.G. The use of empirical Bayes estimators in a linear regression model. Biometrika. 55:1968;525-534.
5. Desouza C.M. An empirical Bayes formulation of cohort models in cancer epidemiology. Stat Med. 10:1991;1241-1256.
6. Fried J. Analyses of deoxyribonucleic acid histograms from flow cytofluorometry-estimation of the distribution of cells within s-shape. J Histochem Cytochem. 25:1977;942-951.
7. Grabski F., Sarhan A. Empirical Bayes estimation in the exponential reliability. Reliab Engng Syst Safety. 53:1996;105-113.
8. Krutchkoff R.G. Empirical Bayes estimation. Am Stat. 26:1972;14-16.
9. Lahiri P., Park D.H. Nonparametric Bayes and empirical Bayes estimators of mean residual life at age t. J Stat Plan Inference. 29:1991;125-136.
10. Lemon G.H. An empirical Bayes approach to reliability. IEEE Trans Reliab. R-21:1972;155-158.
11. Lin P.G. Rates of convergence in empirical Bayes estimation problems. Discrete cases. Ann Inst Stat Math. 24:1972;319-325.
12. Louis T.A. Using empirical Bayes methods in biopharmaceutical research. Stat Med. 10:1991;811-827.
13. Maritz J.S. Smooth empirical Bayes estimation for continuous distribution. Biometrika. 54:1967;417-429.
14. Maritz J.S. Empirical Bayes methods. 1970;Mathuen, London.
15. Martz H.F. Pooling life-test data by means of the empirical Bayes method. IEEE Trans Reliab. R-24:1975;27-30.
16. Martz H.F., Krutchkoff R.G. Empirical Bayes estimators in a multiple linear regression model. Biometrika. 56:1969;367-374.
17. Martz H.F., Wellar R.A. Bayesian reliability analysis. 1982;Wiley, New York.
18. Michols W.G., Tsokos C.P. Empirical Bayes point estimation in a family of probability distributions. Int Stat Rev. 40:1972;146-161.
19. Mollie A., Richardson S. Empirical Bayes estimates of cancer mortality rates using spatial models. Stat Med. 10:1991;95-112.
20. Norberg R. Experience rating in group life insurance Scand. Actuarial J. 1989;194-224.
21. O'Bryan T.E. Some empirical Bayes results in the case of component problems with varying sample sizes for discrete exponential families. Ann Stat. 4:1976;1290-1293.
22. O'Bryan T.E. Rates of convergence in a modified empirical Bayes estimation problem involving Poisson distributions. Commun Stat Theory Meth. A8:1979;167-174.
23. O'Bryan T.E., Susarla V. Empirical Bayes estimations of reliability for lognormal failure model. IEEE Trans Reliab. R-27:1977;332-336.
24. Rutherford J.R., Krutchkoff R.G. Some empirical Bayes techniques in point estimation. Biometrika. 5:1969;133-137.
25. Sarhan A. Empirical Bayes estimates in exponential reliability model. Appl Math and Comp. 2:(135):2003;319-332.
26. Sarhan A. Empirical Bayes estimators of indexed parameters of exponential families. Int J Appl Math. 1:(4):1999;365-371.
27. Sarhan A., Karawia A. Empirical Bayes estimators for the exponential reliability measures. Int J Appl Math. 1:(5):1999;521-528.
28. Susarla V. Empirical Bayes theory, Encyclopedia of statistical sciences. vol. 2:1982;Wiley, New York.
29. Zacks S. The theory of statistical inference. 1970;Wiley, New York.