论文信息 - The Estimation of Pr (Y < X) in the Normal Case

The Estimation of Pr (Y < X) in the Normal Case

The minimum variance unbiased estimator of Pr {Y < X} under the assumption that X and Y are independently normally distributed is derived. Approximations to this “best” estimator are obtained, and these approximations are suggested as alternatives to the asymptotically equivalent estimator used by Church and Harris (1970) to obtain confidence intervals for that probability.

F. Downton

[1] D. Blackwell. Conditional Expectation and Unbiased Sequential Estimation , 1947 .

[2] C. Radhakrishna Rao,et al. Sufficient statistics and minimum variance estimates , 1949, Mathematical Proceedings of the Cambridge Philosophical Society.

[3] Analytical studies in stop-loss reinsurance. II , 1951 .

[4] H. Daniels. Saddlepoint Approximations in Statistics , 1954 .

[5] Ingram Olkin,et al. Unbiased Estimation of Some Multivariate Probability Densities and Related Functions , 1969 .

[6] Morris L. Eaton,et al. The Application of Invariance to Unbiased Estimation , 1970 .

[7] J. D. Church,et al. The Estimation of Reliability from Stress-Strength Relationships , 1970 .

[8] A. Seheult,et al. On Unbiased Estimation of Density Functions , 1971 .