Quadrat Analysis_RW_Thomas

However in many applications of the negative binomial

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Unformatted text preview: g results, and in such instances it is wise to select the maximum likelihood estimate of k. *(iv) Other distributions with a mean and variance defined by (53) (54) Many other probability distributions exist for describing certain types of dependency between points, and most of these distributions can be derived as mixtures of the three basic models we have already discussed: the binomial, the Poisson, and the negative binomial. One interesting example is the Neyman A distribution (Neyman, 1939) which may be derived as a compound model resulting from the mixture of two Poisson processes (see Rogers,1974). This model assumes that if clusters of points are laid down randomly in space such that the average number of points per cluster also follows a Poisson distribution, thentheprobabilityoffinding exactly x points in a specified cell is given by (47) with a mean and variance defined respectively by The moments estimates for a and v are given by (48) (49) (50) (51) Neyman derived this distribution specifically to model the distribution of insect larvae crawling away from recently hatched egg clusters. He assumed that the egg clusters were distributed randomly in space and also that mean number of eggs per clu...
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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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