Probability weighted indices for improved ecosystem report card scoring



This paper outlines a new method for computing an ecosystem index using probability weighted moments (PWMs) in place of conventional moments. Conventional methods of index construction are based on a scaled measure of the discrepancy between the sample mean and a guideline or reference value and as such tend to reflect only gross movements in distributional location. PWMs on the other hand allow for a more targeted assessment through the incorporation of a weighting function specified by the analyst. We refer to the resulting index as a probability weighted index or PWI. Although all data are used in the computation of the PWI, they do not necessarily contribute equally to the final result as is the case with conventional moments. Computational formulae and associated R code are provided, which allow the PWIs and their standard errors to be unbiasedly estimated from empirical data. Copyright © 2014 John Wiley & Sons, Ltd.