1 1 1 1 x x 012 when 1 we get the geometric density

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1 1 1 1 x , x 0,1,2, .... When 1 we get the geometric density [because Γ 1 1 and Γ 1 x x !]. Can show that, as 0, the density converges to the Poisson density. It can be shown that E X Var X 1   2 33
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Thus, we can write Var X E X 1  and so is a measure of overdispersion. For a given , as increases, Var X / E X increases. Later, when we turn to statistics, we will see that if we fix (for example, 1 in the geometric) – that is, we assume we know it – then estimating from a sample of data is easy. The problem is considerably harder when and both need to be estimated. We will write X ~ NegBin , . 34
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