|
Abstract:
|
In many fields of study scientists are interested in estimating the number of unobserved classes. For instance, a biologist may want to find the number of rare species of an animal population in order to study biodiversity. Based on the traditional negative binomial model for this data (Fisher, Corbet, and Williams 1943), we propose a model assuming that the number of individuals from each class are independent Poisson samples, and that the means of these Poisson random variables follow a finite mixture of exponential distributions. We fit the proposed model using a nested EM algorithm and incorporate Aitken's acceleration in a mixture of three exponentials. Microbial samples from the coast of Massachusetts Bay near Nahant, Massachusetts are analyzed to demonstrate that the model produces reasonable estimates and fits the data satisfactorily.
|
