Counts on the number of items per cluster (or colony or group) must necessarily be
Chapter 14, Problem 14.38(choose chapter or problem)
Counts on the number of items per cluster (or colony or group) must necessarily be greater than or equal to 1. Thus, the Poisson distribution generally does not fit these kinds of counts. For modeling counts on phenomena such as number of bacteria per colony, number of people per household, and number of animals per litter, the logarithmic series distribution often proves useful. This discrete distribution has probability function given by p(y | ) = 1 ln(1 ) y y , y = 1, 2, 3,..., 0 << 1, where is an unknown parameter. a Show that the MLE of satisfies the equation Y = (1 ) ln(1 ) , where Y = 1 n n i=1 Yi .
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