Virtual Math. Colloq. Apr. 9 3:30pm
Friday, April 9th at 3:30pm, Virtual Room (Zoom Meeting ID: 824 5840 4119)
"Properties and Computation of Maximum Likelihood Estimates for the Negative Binomial Distribution"
Professor Ryan Gill, University of Louisville
The negative binomial distribution is widely-used to model count data where it is suspected that there is overdispersion in which the variance exceeds the mean. In 1950, Anscombe conjectured that the maximum likelihood estimate of two parameters in the negative binomial is unique when the sample variance exceeds the sample mean and does not exist otherwise. In this talk, a proof by Simonsen is discussed, and it is shown how his work can be extended to show that the Newton-Raphson algorithm is guaranteed to converge to the MLE if an appropriate starting value is chosen.