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 JAMP  Vol.4 No.2 , February 2016
The Confidence Distribution Method to the Behrens-Fisher Problem
Abstract: We use the methods of “The Welch-Satterthwaite test”, “The Cochran-Cox test”, “The Generalized p-value test”, “Computational Approach test” to structure different Confidence Distributions, and use the Confidence Distributions to give an new solution the confidence interval of the difference between two population means where the populations are assumed to be normal with unknown and unequal variances. Finally, we find the most effective solution through the numerical simulation.
Cite this paper: Tao, W. and Ye, W. (2016) The Confidence Distribution Method to the Behrens-Fisher Problem. Journal of Applied Mathematics and Physics, 4, 286-293. doi: 10.4236/jamp.2016.42036.
References

[1]   Xu, J.Q. (2011) The Generalized Confidence Interval of the Behrens-Fisher Problem. Statistics and Decision, 2, 29-30.

[2]   Xie, M.G. and Singh, K. (2013) Confidence Distribution, the Frequentist Distribution Estimator of a Parameter: A Review. International Statistical Review, 81, 3-39.

[3]   Schweder, T. and Hjort, N.L. (2002) Confidence and Likelihood. Scandinavian Journal of Statistics, 29, 309-332.
http://dx.doi.org/10.1111/1467-9469.00285

[4]   Singh, K., Xie, M. and Strawderman, W.E. (2005) Combining Information from Independent Sources through Confidence Distributions. Annals of Statistics, 33, 159-183.
http://dx.doi.org/10.1214/009053604000001084

[5]   Singh, K., Xie, M. and Strawderman, W.E. (2007) Confidence Distribution (CD)—Distribution Estimator of a Parameter. Complex Datasets and Inverse Problems, 54, 132-150.
http://dx.doi.org/10.1214/074921707000000102

[6]   Welch, B.L. (1949) Further Notes on Mrs. Aspin’s Tables. Biometrika, 36, 293-296.

[7]   Satterthwaite, F.E. (1946) An Approximate Distribution of Estimates of Variance Components. Biometrics Bulletin, 2, 110-114.
http://dx.doi.org/10.2307/3002019

[8]   Cochran, W.G. and Cox, G.M. (1950) Experimental Designs. John Wiley and Sons, New York.

[9]   Weerahandi, S. (1994) Exact Statistical Methods for Data Analysis (174-181). Springer Series in Statistics, Springer-Verlag, New York.

[10]   Chang, C.H. and Pal, N. (2008) A Revisit to the Behrens-Fisher Problem: Comparison of Five Test Methods. Communications in Statistics—Simulationand Computation, 37, 1064-1085.

[11]   Singh, K., Xie, M. and Strawderman, W. (2001) Confidence Distributions—Concept, Theory and Applications. Technical Report, Dept. of Statistics, Rutgers University, New Jersey, USA.

 
 
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