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Negative Binomial Quadrat Counts and Point Processes
Peter J. Diggle and Robin K. Milne
Scandinavian Journal of Statistics
Vol. 10, No. 4 (1983), pp. 257-267
Published by: Wiley on behalf of Board of the Foundation of the Scandinavian Journal of Statistics
Stable URL: http://www.jstor.org/stable/4615928
Page Count: 11
You can always find the topics here!Topics: Binomials, Binomial distributions, Poisson process, Statism, Ergodic theory, Tessellations, Random variables, Additivity, Probabilities, Approximation
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Implicit in the fitting of negative binomial distributions to quadrat count data is an assumption, based partly on additivity, that if the areas of the quadrats are systematically changed then the fitting of another negative binomial distribution would be appropriate. It is therefore of interest to exhibit suitable probability models for which consistency with the additivity can be demonstrated. This leads to a search for point processes with negative binomial one-dimensional distributions and in particular for such processes which are in addition stationary, ergodic, and orderly. The paper fails to exhibit any negative binomial point process possessing all three of these properties and the authors now believe that no such process exists. However, it summarizes the present state of knowledge, including some discussion of approximations, and attempts to clarify the problems involved in what seems a difficult area.
Scandinavian Journal of Statistics © 1983 Board of the Foundation of the Scandinavian Journal of Statistics