3.3. Aggregated spatial distributions

   There is no universal theoretical model for aggregated spatial distributions.
   However, there are empirical models, e.g., negative binomial distribution (NBD)
   which work very well in the majority of cases. NBD is described by the equation:

                                     [eqnbd1.gif]

   where m is mean, k is "coefficient of aggregation" (aggregation increases with
   decreasing k). The zero term (the proportion of empty samples) equals to:

                                     [eqnbd0.gif]

   Other terms can be estimated by iteration:

                                     [eqnbd3.gif]

   Estimating NBD parameters using the method of moments:

                                         m = M

                                     [eqnbdk.gif]

   For a random distribution, CD=1 and k is infinite. When k increases to infinity
   then NBD distribution coincides with poisson distribution.

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   [4]Alexei Sharov 12/28/95

References

   1. http://alexei.nfshost.com/PopEcol/lec3/random.html
   2. http://alexei.nfshost.com/PopEcol/lec3/spatdist.html
   3. http://alexei.nfshost.com/PopEcol/lec3/agindex.html
   4. http://alexei.nfshost.com/~sharov/alexei.html