Quadrat Analysis_RW_Thomas

The negative binomial is derived in the following

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Unformatted text preview: infinite grid independently of time. However, as distinct from the assumptions of the binomial, we now assume that the probability of a point being placed in a specified cell increases linearly with the number of points already placed in that cell. Consequently, at any one point in time, the probabilities of cells receiving a point are not equal, but are directly related to the existing distribution. Naturally this process will generate a clustered distribution, and it can be proved (see Rogers, 1974, p.16) that probability distribution embodying these assumptions, such that the proability of a specified cell containing exactly x points is, given by (37) (38) (39) (40) It can be seen that the probabilities predicted by equation (37) are dependent clustering associated with the contagious process, and its exact value is specified within the limits zero to infinity. As k tends to infinity the clustering disappears and the negative binomial tends to the Poisson distribution, and as k approaches zero the distribution converges on an exceptionally clustered logarithmic distribution (see Bliss and Fisher, 1953). Inspection of the variance/mean ratio for this distribution ((39)/38)) shows that its When k is...
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This note was uploaded on 02/15/2012 for the course GEO 6938 taught by Professor Staff during the Summer '08 term at University of Florida.

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