Some Topics Related to Diversity Indices and Applications

Abstract

This thesis discusses three diversity measures: Simpson's Index, Shannon's Index and Berger–Parker Dominance as well as their corresponding True diversity. Evenness measures the balance of a community which carries different information from diversity indices. We give an example on the application of diversity indices by comparing the surname diversity of China and USA. We also use OLS regression to investigate whether diversified investment strategy leads to higher return rate for mutual funds. Our analysis shows that funds that are diversified in investment have higher return rate. Although highly diversified investment does not translate into high return directly, the market where equity enters also plays an important role. Our analysis reveals the potential of investment diversity and provides motivation for diversifying investment strategy. The diversity indices also have the ability of discriminating categories. With linear discriminant analysis (LDA) and classification tree method, we use Simpson's index and year to date return rate to successfully differentiate mutual fund category. In the last part of the thesis, we introduce the Bayesian approach to estimate diversity indices from an observed sample. We propose four estimators of Simpson's Index based on the sampling distribution of relative abundance and investigate their estimating ability.