Bayes and empirical bayes estimation of the probability that z > x + y

References

• Blackwell , D. 1973 . Discreteness of Ferguson selections . Ann. Statist , 1 : 356 – 358 .
   Web of Science ®Google Scholar
• Blackwell , D. and Macqueen , J.B. 1973 . Ferguson distribution via polya urn schemes . Ann. Statist , 1 : 353 – 355 .
   Web of Science ®Google Scholar
• Blum , J.R. and Susarla , V. 1977 . On the posterior distribution of a Dirichlet process given randomly right censored observations . Stochastic Process and their Applications , 5 : 207 – 211 .
   Google Scholar
• Chen , Y.Y. , Hollander , M. and Langberg , N.A. 1983 . Testing whetehr new is better than used with randomly censored data . Ann. Statist , 11 : 267 – 274 .
   Web of Science ®Google Scholar
• Ferguson , T.S. 1973 . A Bayesian analysis of some non–parametric problems . Ann. Statist , 1 : 209 – 230 .
   Web of Science ®Google Scholar
• Ferguson , T.S. 1983 . “ Bayesian density estimation by mixtures of normal distributions ” . In Recent Advances in Statistics , Academic Press .
   Google Scholar
• Hoeffding , W.A. 1948 . A Class of Statistics with asymptotially normal distribution . Ann. Math. Statis , 19 : 293 – 325 .
   Google Scholar
• Hoeffding , W.A. 1963 . Probability inequalities for sums of bounded random variables . J. Amer. Statist. Assoc , 58 : 13 – 30 .
   Web of Science ®Google Scholar
• Hollander , M. and Proschan , F. 1972 . Testing whether new is better than used . Ann. Math. Statist , 43 : 1136 – 1146 .
   Google Scholar
• Hollander , M. and Korwar , R.M. 1976 . Nonparametric empirical Bayes estimation of the probability that x≤y . Commun. Statist. –Theor. Meth , A5 ( 14 ) : 1369 – 1383 .
   Google Scholar
• Kaplan , E.L. and Meier , P. 1958 . Nonparametric estimation from incomplete observations . J. Amer. Statist. Assoc , 53 ( 14 ) : 457 – 481 .
   Google Scholar
• Phadia , E.G. and Susarla , V. 1979 . An empirical Bayes approach to two sample problems with censored data . Commun. Statist. –Theor. Meth , A8 ( 13 ) : 1327 – 1351 .
   Web of Science ®Google Scholar
• Sethuraman , J. and Tiwari , Ram C. 1982 . “ Convergence of Dirichlet measures and the interpretaitons of their parameter ” . In Statistical Decision Theory and Related Topics, III , Edited by: Gupta , S.S. and Berger , James O. Vol. 2 , Academic Press .
   Google Scholar
• Tiwari Ram C. A mathematical study of the Dirichlet process Department of Statistics, Florida State University 1981 Ph. D. Dissertation
   Google Scholar
• Zehwirth , B. 1981 . A note on the asymptotic optimality of the empirical Bayes distribution function . Ann. Statist , 9 : 221 – 224 .
   Google Scholar