Ryan Gill, PhDDepartment of Mathematics, University of Louisville

"Computation of Maximum Likelihood Estimates for the Negative Binomial Distribution"

In this talk, maximum likelihood estimation of the parameters of the negative binomial distribution are discussed.  Literature concerning the existence and uniqueness of a solution to the likelihood equation is summarized.  In the case where the MLE exists, it is shown that the Newton-Raphson algorithm is guaranteed to converge to the MLE if an appropriate starting value is chosen. 

Examples are given to compare this method with others from the literature.

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