Inference on Measures of Niche Overlap for Heteroscedastic Normal Populations

Abstract

SYNOPTIC ABSTRACTEcologists and economists have long been interested in measures of overlap between two populations to study disparities between resource utilizations or incomes of two groups. Also sociologists have been interested in spatial segregation of social groups, particularly racial and occupational groups. While the measures of overlap under the assumption of homogeneity of variances have received a good deal of attention, little has been written about the overlap of heteroscedastic populations. Three different measures of niche overlap between two normally distributed populations are studied in this paper. Estimation of overlap under general conditions of heterogeneity of variances is discussed. The expressions for approximate bias and variance of estimates are derived using both MLE, and unbiased estimators of population variances. The proximity of variance and bias estimates computed using the estimates of overlap coefficients to that using the actual values is studied using simulation techniques.