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−1−1−1−1x,x0,1,2,....∙When1 we get the geometric density [becauseΓ11 andΓ1xx!]. Can show that, as→0, the density converges to thePoissondensity.∙It can be shown thatEXVarX1233
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Thus, we can writeVarXEX1and sois a measure of overdispersion. For a given, asincreases,VarX/EXincreases.∙Later, when we turn to statistics, we will see that if we fix(forexample,1 in the geometric) – that is, we assume we know it –then estimatingfrom a sample of data is easy. The problem isconsiderably harder whenandboth need to be estimated.∙We will writeX~NegBin,.34