Estimation for the negative binomial distribution based on the conditional likelihood

References

• Andersen , E. B. 1970 . Asymptotic properties of conditional maximum-1ike 1ihood estimators . Journal of the Royal Statistical Society B , 32 : 283 – 301 .
   Google Scholar
• Anscombe , F. J. 1950 . Sampling theory of the negative binomial and logarithmic series distributions . Biometrika , 37 : 358 – 382 .
   PubMed Web of Science ®Google Scholar
• Barnwal , R K. and Paul , S. R. 1988 . Analysis of the one-way layout of count data with negative binomial variation . Biometrika , 75 : 215 – 222 .
   Web of Science ®Google Scholar
• Bowman , K. O. 1984 . Extended moment series and the parameters of the negative binomial distribution . Biometrics , 40 : 249 – 252 .
   Web of Science ®Google Scholar
• Clark , S. J. and Perry , J. N. 1984 . Estimation of the negative binomial parameter k by maximum quasi-1ikelihood . Biometrics , 45 : 309 – 316 .
   Web of Science ®Google Scholar
• Cox , D. R. and Reid , N. 1987 . Parameter orthogonality and approximate conditional inference(with discussion) . Journal of the Royal Statistical Society B , 49 : 1 – 39 .
   Google Scholar
• Fishman , G. S. 1978 . Principle of Discrete Event Simulation , New York : Wiley .
   Google Scholar
• Johnson , N. L. and Kotz , S. 1969 . Distributions in Statistics: Discrete Distributions , New York : Wiley .
   Google Scholar
• Kalbfleisch , J. D. and Sprott , D. A. 1973 . Marginal and conditional likelihoods . Sankhya A , 35 : 311 – 328 .
   Google Scholar
• Lawless , J. F. 1987 . Negative binomial and mixed Poisson regression . The Canadian Journal of Statistics , 15 : 209 – 225 .
   Web of Science ®Google Scholar
• Levin , B. and Reeds , J. 1977 . Compound multinomial likelihood functions are unimodal :Proof of a conjecture of I.J. Good . The Annals of Statistics , 5 : 79 – 87 .
   Web of Science ®Google Scholar
• Margolin , B.H. , Kaplan , N. and Zieger , E. 1981 . Statistical analysis of the Ames salmonella/microsome test . Proceedings of the National Academy of Sciences USA , 78 : 3779 – 3783 .
   PubMed Web of Science ®Google Scholar
• Pieters , E. P. , Gates , C. E. , Matis , J.H. and Sterling , W. L. 1977 . Small sample comparison of different estimators of negative binomial parameters . Biometrics , 33 : 718 – 723 .
   Web of Science ®Google Scholar
• Taylor , L. R. , Woiwod , I. P. and Perry , J.N. 1979 . The negative binomial as a dynamic ecological model for aggregation and the density-dependence of k . Journal of Animal Ecology , 48 : 289 – 304 .
   Web of Science ®Google Scholar
• Willson , L. J. , Folks , J. L. and Young , J. H. 1984 . Multistage estimation compared with fixed-sample-size estimation of the negative binomial parameter k . Biometrics , 40 : 109 – 117 .
   Web of Science ®Google Scholar
• Yanagimoto , T. 1987 . A notion of an obstructive residual likelihood . Annals of the Institute of Statistical Mathematics , 39 : 247 – 261 .
   Web of Science ®Google Scholar