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Tan, W. Y.; Balakrishnan, N.

Bayesian approach to robust comparison of two means based on asymmetric type-II censored samples. (English) Zbl 0649.62028

J. Stat. Comput. Simulation 30, No. 2, 81-102 (1988).
By adopting Bayesian method, we develop a robust procedure for comparing two means when variances are unequal based on asymmetric type-II censored samples and assuming normality for the censored samples. The posterior distribution of the difference \(\delta\) of means is derived and approximated. Bayesian interval for \(\delta\) is then obtained and used to make inference about \(\delta\) ; further, the effects of asymmetric censoring on the posterior probabilities are assessed. These results are finally applied to Lehmann’s data and to Brownlee’s data. The results display that the effects of asymmetric censoring are in general quite small.

Cited in 1 Document

MSC:

62F15 Bayesian inference
62F35 Robustness and adaptive procedures (parametric inference)

Keywords:

unequal variances; Behrens-Fisher problem; robust procedure; comparing two means; normality; asymmetric censoring; posterior probabilities
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References:

[1] Balakrishnan N., Biometrical J (1988)
[2] Box, G. E. P. and Tiao, G. C. 1973. ”Bayesian Inference in Statical Analysis”. Don Mills, Ontario: Addison–Wesely. · Zbl 0271.62044
[3] Brownlee, K. A. 1965. ”Statistical Theory and Methodology in Science and Engineering”. New York: John Wiley. · Zbl 0136.39203
[4] DOI: 10.2307/1266442 · doi:10.2307/1266442
[5] Gupta A. K., Biometrika 39 pp 260– (1952) · Zbl 0048.12004 · doi:10.1093/biomet/39.3-4.260
[6] Lehmann, E. L. 1975. ”Nonparametrics: Statistical Methods Based on Ranks”. New York: McGraw Hill. · Zbl 0354.62038
[7] DOI: 10.1016/0378-3758(85)90038-2 · doi:10.1016/0378-3758(85)90038-2
[8] DOI: 10.1080/00949658608810887 · Zbl 0616.62046 · doi:10.1080/00949658608810887
[9] Tiku M. L., Biometrika 54 pp 155– (1967) · doi:10.1093/biomet/54.1-2.155
[10] DOI: 10.1093/biomet/57.1.207 · Zbl 0193.16703 · doi:10.1093/biomet/57.1.207
[11] Tiku M. L., Biometrika 29 pp 25– (1973) · doi:10.2307/2529673
[12] DOI: 10.1016/0378-3758(80)90002-6 · Zbl 0441.62035 · doi:10.1016/0378-3758(80)90002-6
[13] Tiku M. L., Proc. Internat. Symp. on Statistics and Related Topics pp 297– (1980)
[14] DOI: 10.1002/bimj.4710240610 · Zbl 0495.62049 · doi:10.1002/bimj.4710240610
[15] DOI: 10.1080/03610918208828405 · Zbl 0503.62030 · doi:10.1080/03610918208828405
[16] DOI: 10.1080/03610928108828173 · Zbl 0467.62032 · doi:10.1080/03610928108828173
[17] Tiku, M. L., Tan, W. Y. and Balakrishnan, N. 1986. ”Robust Inference”. New York: Marcel Dekker.
[18] Zellner, A. 1971. ”An Introduction to Bayesian Inference in Econometrics”. New York: John Wiley. · Zbl 0246.62098
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