Tests and Diagnostics for Heterogeneity in the Species Problem
Changxuan Mao and Bruce G. Lindsay
Suppose a random sample of individuals is drawn from a population with N disjoint classes. The population is said to be homogeneous when all the classes have the same abundance. Otherwise, it is said to be heterogeneous. The number of individuals from each class in the sample is assumed to be Poisson distributed. There is a vast literature towards the estimation of N. Although the performance of estimators is related to the homogeneity assumption, testing homogeneity has received little investigation. In this paper, we rst discuss the 2 goodness-of- t test. Next, a dispersion score test is presented and two graphic diagnostics are developed to detect the existence of heterogeneity. Two datasets from epidemiological and genomic studies are used to illustration of these tests and diagnostics.
Key Words Number of species; Poisson mixture; Heterogeneity; Graphical diagnostics.