Efficient Estimation of Parameters of the Negative Binomial Distribution

References

• Anscombe , F. J. ( 1949 ). The statistical analysis of insect counts based on the negative binomial distribution . Biometrics 5 : 165 – 173 . [CSA]
   PubMed Web of Science ®Google Scholar
• Anscombe , F. J. ( 1950 ). Sampling theory of the negative binomial and logarithmic series distributions . Biometrika 37 : 358 – 382 . [INFOTRIEVE] [CSA] [CROSSREF]
   PubMed Web of Science ®Google Scholar
• Arbous , A. , Kerrich , J. ( 1951 ). Accident statistics and the concept of accident proneness . Biometrics 7 : 340 – 432 . [CSA]
   Web of Science ®Google Scholar
• Barndorff-Nielsen , O. , Yeo , G. ( 1969 ). Negative binomial processes . J. Appl. Probability 6 : 633 – 647 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Bondesson , L. ( 1992 ). Generalized Gamma Convolutions and Related Classes of Distributions and Densities . New York : Springer-Verlag .
   Google Scholar
• Ehrenberg , A. ( 1988 ). Repeat-Buying: Facts, Theory and Applications . London : Charles Griffin & Company Ltd .; New York : Oxford University Press .
   Google Scholar
• Fisher , R. A. ( 1941 ). The negative binomial distribution . Ann. Eugenics 11 : 182 – 187 . [CSA]
   Google Scholar
• Grandell , J. ( 1997 ). Mixed Poisson Processes . London : Chapman & Hall .
   Google Scholar
• Greenwood , M. , Yule , G. ( 1920 ). An inquiry into the nature of frequency distributions representative of multiple happenings with particular reference to the occurrence of multiple attacks of disease or of repeated accidents . J. Roy Statist. Soc. 93 : 255 – 279 . [CSA]
   Google Scholar
• Haldane , J. B. S. ( 1941 ). The fitting of binomial distributions . Ann. Eugenics 11 : 179 – 181 . [CSA]
   Google Scholar
• Johnson , N. L. , Kotz , S. , Kemp , A. W. ( 1992 ). Univariate Discrete Distributions . New York : John Wiley & Sons Inc .
   Google Scholar
• Kendall , D. G. (1948a). On some modes of population growth leading to R. A. Fisher's logarithmic series distribution. Biometrika 35:6–15. [CSA] [CROSSREF]
   PubMed Web of Science ®Google Scholar
• Kendall , D. G. ( 1948b ). On the generalized “birth-and-death” process . Ann. Math. Statist. 19 : 1 – 15 . [CSA]
   Google Scholar
• Lundberg , O. ( 1964 ). On Random Processes and Their Application to Sickness and Accident Statistics . Uppsala : Almquist and Wiksells .
   Google Scholar
• Savani , V. , Zhigljavsky , A. ( 2006 ). Efficient parameter estimation for independent and INAR(1) negative binomial samples . Metrika (Accepted for publication) . [CSA]
   Web of Science ®Google Scholar
• Serfling , R. J. ( 1980 ). Approximation Theorems of Mathematical Statistics . New York : John Wiley & Sons Inc .
   Google Scholar