On Bayesian Estimation of the Product of Poisson Rates with Application to Reliability

References

• Chen , M. H. , Shao , Q. M. ( 1999 ). Monte Carlo estimation of Bayesian credible and HPD intervals . J. Comp. Graph. Statist. 8 : 69 – 92 . [CSA]
   Web of Science ®Google Scholar
• Chen , M. H. , Shao , Q. M. , Ibrahim , J. G. ( 2000 ). Monte Carlo Methods in Bayesian Computation . New York : Springer .
   Google Scholar
• Cox , D. R. , Reid , N. ( 1987 ). Parameter orthogonality and approximate conditional inference (with discussion) . J. Roy. Statist. Soc. B 49 : 1 – 39 . [CSA]
   Google Scholar
• Datta , G. S. , Ghosh , M. ( 1996 ). On the invariance of noninformative priors . Ann. Statist. 24 : 141 – 159 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Datta , G. S. , Ghosh , M. , Mukerjee , R. ( 2000 ). Some new results on probability matching priors . Calcutta Statistical Assoc. Bull. 50 : 179 – 192 . [CSA]
   Google Scholar
• Environmental Protection Agency . ( 1986 ). Bacteriological ambient water quality criteria for marine and fresh recreational waters . Ambient Water Quality Criteria for Bacteria . 1986, United States Environmental Protection Agency Report No. EPA440/5-84-002, Washington. (http://www.epa.gov./waterscience/beaches/1986crit.pdf . [CSA]
   Google Scholar
• Harris , B. ( 1971 ). Hypothesis testing and confidence intervals for products and quotients of Poisson parameters with applications to reliability . J. Amer. Statist. Assoc. 66 : 609 – 613 . [CSA]
   Web of Science ®Google Scholar
• Harris , B. , Soms , A. P. ( 1973 ). The reliability systems of independent parallel components when some components are repeated . J. Amer. Statist. Assoc. 68 : 894 – 898 . [CSA]
   Web of Science ®Google Scholar
• Hwang , D. S. ( 1971 ). Interval estimation of functions of Bernoulli parameters with reliability and biomedical applications . University of Minnesota, School of Statistics Technical Report No. 152 , Minneapolis .
   Google Scholar
• Kenneth , V. D. , John , S. D. , Kenneth , J. S. ( 1998 ). Incorporating a geometric mean formula into CPI . Monthly Labor Review, October, 2–7.
   Google Scholar
• Leemis , L. M. , Trivedi , K. S. ( 1996 ). A comparison of approximate interval estimators for Bernoulli parameter . Amer. Statistician 50 : 63 – 68 . [CSA]
   Web of Science ®Google Scholar
• Lehmann , E. I. ( 1959 ). Testing Statistical Hypotheses . New York : John Wiley & Sons .
   Google Scholar
• Madansky , A. ( 1965 ). Approximate confidence limits for the reliability of series and parallel systems . Technometrics 7 : 495 – 503 . [CSA]
   Web of Science ®Google Scholar
• Martz , H. F. , Waller , R. A. (1982). Bayesian Reliability Analysis . New York : John Wiley & Sons.
   Google Scholar
• Mukerjee , R. , Ghosh , M. ( 1997 ). Second order probability matching priors . Biometrika 84 : 970 – 975 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Mukerjee , R. , Reid , N. ( 1999 ). On a property of probability matching priors: matching the alternative coverage probabilities . Biometrika 86 : 333 – 340 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Page , C. F. ( 1990 ). Allocation proportional to coefficients of variation when estimating the products of parameters . J. Amer. Statist. Assoc. 85 : 1134 – 1139 . [CSA]
   Google Scholar
• Stein , C. ( 1985 ). On the coverage probability of confidence sets based on a prior distribution . Sequential Methods in Statistics . Vol. 19 , Warsaw : Banach Center Publications, PWN-Polish Scientific Publishers , pp. 485 – 515 .
   Google Scholar
• Sun , D. , Ye , K. ( 1995 ). Reference prior Bayesian analysis for normal mean . J. Amer. Statist. Assoc. 90 : 589 – 597 . [CSA]
   Web of Science ®Google Scholar
• Tibshirani , R. ( 1989 ). Noninformative priors for one parameter of many . Biometrika 76 : 604 – 608 . [CSA]
   Web of Science ®Google Scholar
• Welch , B. L. , Peer , H. W. ( 1963 ). On formulae for confidence points based on integrals of weighted likelihoods . J. Roy. Statist. Soc. B 25 : 318 – 329 . [CSA]
   Google Scholar
• Ye , K. , Berger , J. ( 1991 ). Noninformative priors for inferences in exponential regression models . Biometrika 78 : 645 – 656 . [CSA]
   Web of Science ®Google Scholar