Assessing diversity over time via functional data analysis and related tools

The problems of measuring and monitoring diversity have been widely discussed in recent decades; nevertheless, both theoretical perspectives and empirical results appear conflicting and inconsistent in ecology, management, business administration, social science, and other disciplines that deal with this concept that is multidimensional and multivariate in nature. The aim is to reconsider the problem of assessing diversity from a statistical perspective for solving some inconsistency of the classical diversity indices. We start from the concept of diversity profile and Hill’s number integral function, which are monotone parametric functions useful to represent the concept of diversity of a specific community and develops a procedure for treating these curves in a functional context. Exploiting Hill’s numbers, functional data analysis, and the monotone smoothing approach via B-splines, different functional instruments are proposed for assessing diversity changes over time and comparing the state of variety with respect to a benchmark. The main purpose is to provide human resources specialists, scholars, and ecologists with additional tools to improve the understanding of the dynamics of diversity within organizations, ecological communities, or other statistical samples where the role of diversity is worthy to be inspected.