A new class of modified binomial distributions with applications to certain toxicological experimentsFootnote^∗

^∗The views expressed in this paper are those of the author and not necessarily of the Food and Drug Administration.

References

• Altham , P. M. E. 1978 . Two generalizations of the binomial distribution . Applied Statistics , 27 : 162 – 167 .
   Google Scholar
• Bahadur , R. R. 1961 . “ A representation of the joint distribution of responses to n dichotomous items ” . In In: Studies in Item Analysis and Prediction , Edited by: Solomon , H. Stanford, California : Stanford University Press .
   Google Scholar
• Chatfield , C. and Goodhardt , G. J. 1970 . The beta-binomial model for consumer purchasing behavior . Applied Statistics , 19 : 240 – 250 .
   Web of Science ®Google Scholar
• Darroch , J. N. 1974 . Multiplicative and additive interaction in contingency tables . Biometrika , 61 : 207 – 214 .
   Web of Science ®Google Scholar
• Drinkwater , N. R. and Klotz , J. 1981 . Statistical methods for the analysis of tumor multiplicity data . Cancer Research , 41 : 113 – 119 .
   PubMed Web of Science ®Google Scholar
• Griffiths , D. A. 1973 . Maximum likelihood estimation for the beta-binomial distribution and an application to the household distribution of the total number of cases of a disease . Biometrics , 29 : 637 – 648 .
   PubMed Web of Science ®Google Scholar
• Haseman , J. K. and Kupper , L. L. 1979 . Analysis of dichotomous response data from certain toxicological experiments . Biometrics , 35 : 281 – 293 .
   PubMed Web of Science ®Google Scholar
• Haseman , J. K. and Soares , E. R. 1976 . The distribution of fetal death in control mice and its implications on statistical tests for dominant lethal effects . Mutation Research , 41 : 277 – 288 .
   PubMed Web of Science ®Google Scholar
• Horsnell , G. 1957 . Economic acceptance sampling schemes . Journal of the Royal Statistical Society, Series A , 120 : 148 – 191 .
   Google Scholar
• Johnson , N. L. and Kotz , S. 1969 . Distributions in Statistics: Discrete Distributions , Boston : Houghton Mifflin Company .
   Google Scholar
• Kemp , C. D. and Kemp , A. W. 1956 . The analysis of point quadrant data . Aust. J. Botany , 4 : 167 – 174 .
   Google Scholar
• Kupper , L. L. and Haseman , J. K. 1978 . The use of a correlated binomial model for the analysis of certain toxicological experiments . Biometrics , 34 : 69 – 76 .
   PubMed Web of Science ®Google Scholar
• Kupper , L. L. , Portier , C. , Hogan , M. D. and Yamamoto , E. 1986 . The impact of litter effects on dose-response modeling in teratology . Biometrics , 42 : 85 – 98 .
   PubMed Web of Science ®Google Scholar
• Luning , K. G. , Sheridan , W. , Ytterborn , K. H. and Gullberg , U. 1966 . The relationship between the number of implantations and the rate of intrauterine death in mice . Mutation Research , 3 : 444 – 451 .
   PubMed Web of Science ®Google Scholar
• Prentice , R. L. 1986 . Binary regression using an extended Beta-Binomial distribution, with discussion of correlation induced by covariate measurement errors . Journal of the American Statistical Association , 81 : 321 – 327 .
   Web of Science ®Google Scholar
• Segreti , A. C. and Munson , A. E. 1981 . Estimation of the median lethal dose when responses within a litter are correlated . Biometrics , 37 : 153 – 156 .
   PubMed Web of Science ®Google Scholar
• Williams , D. A. 1975 . The analysis of binary responses from toxicological experiments involving reproduction and teratogenicity . Biometrics , 31 : 949 – 952 .
   PubMed Web of Science ®Google Scholar