Quadrat Analysis_RW_Thomas

A redundancy of zero indicates a perfect

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Unformatted text preview: urs when the pattern is totally controlled, and this upper limit is achieved by totally uniform and, under certain conditions, totally clustered patterns. Such patterns are totally controlled by unhypothesised information and may easily be reproduced by simple mechanical rules. Unlike other indices of point pattern dispersion, redundancy does not discriminate between clustered and uniform patterns, because in their extreme cases both tend to a redundancy of one. However, a theoretical property of the entropy-maximising geometric distribution helps remedy this deficiency. When the negative binomial k parameter takes on a value of one the negative binomial is identical to the geometric distribution. Therefore, in cases where the Bose-Einstein definition of equal likelihood is appropriate, we can define all observed patterns with estimated k parameters (from equation (45)) of less than one as tending to be clustered, and all other patterns as tending to be uniform. Incidentally, the fact that the negative binomial is equivalent to the geometric distribution when k equals one, vividly illustrates the degree of dif...
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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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