Quadrat Analysis_RW_Thomas

It is useful to re state this problem in terms of the

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Unformatted text preview: ely meso-state. Here we wish to find that probability distribution whose individual probabilities (P m ) maximise the value of Shannon's measure of the entropy of a probability distribution (Shannon and Weaver, 1949) given by gives a close approximation to the probabilities obtained from equation (65). Indeed, the approximation holds for quite small values of n and r. It is interesting to note that the geometric distribution is the discrete form of the negative exponential distribution (where m is a continuous variable) which is the entropy function in Wilson's (1970) family of spatial interaction models. By abandoning the assumption that points are placed in cells independently of one another through time, we have deduced a probability distribution that gives a quite different prediction for the most likely frequency array than the binomial or Poisson. The difference between the binomial and the Bose-Einstein distribution arises because the binomial model assumes the points are distinguishabl...
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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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