Quantifying Diversity and Skewness through some new Efficient Measures: Comparison, Properties and Applications

Abstract

This study aims at developing novel procedures capable of performing more efficiently in complex situations. Overall, our research advances the existing literature on three fronts. Firstly, exploiting the ratio of total number of individuals to the maximum number of individuals, we propose new non-explicit spatial measures to quantify diversity and the extent of distributional evenness (named as Z – A evenness/diversity index) prevalent among various biological species with respect to their natural habitats. The legitimacy of the presented index is established by employing numerous literature based criteria required to maintain by any index to be valid evenness index. The proposed evenness index clears most of the checks, thus presenting itself as a valid measure. Also, number of deaths by COVID-19 data has been utilized to fit distributions and check spatial evenness in the six regions defined by World Health Organization (WHO). The extent of evenness measured through nine evenness indices is lower, highlighting the dissimilar deaths severity in the regions. Secondly, we devise novel measure with minimal assumptions based on cumulative distribution function to assess the underlying amount of skewness – a distributional feature much related to biodiversity – observant in the data. The validity of the proposed measure is established by conforming various desirable characteristics documented in the literature. The extensive comparative analyses declare the proposed measure as valid. Lastly, we delineate the use of auxiliary information to construct enhanced efficient estimators of the newly proposed skewness functional by exploiting the use of ratio estimator, product estimator and difference estimator. The difference estimator based skewness estimator proved itself as more efficient estimator. Throughout this research, the mathematical developments are verified through rigorous simulations encompassing diverse parametric settings. The applicability of proposed methods is demonstrated by using data sets from various fields of scientific research. The gains are then highlighted by conducting vibrant comparative analysis of every development resultant from this study with existing techniques.