Mathematics, Vol. 12, Pages 507: On the Optimal Point of the Weighted Simpson Index

Mathematics, Vol. 12, Pages 507: On the Optimal Point of the Weighted Simpson Index

Mathematics doi: 10.3390/math12040507

Authors: José Pinto Casquilho Helena Mena-Matos

In this short communication, following a brief introduction, we undertake a comprehensive analytical study of the weighted Simpson index. Our primary emphasis concerns the precise determination of the optimal point (minimizer) coordinates and of the minimum value of the index, a differentiable convex function, which is related to the harmonic mean concept. Furthermore, we address and solve the inversion problem and show the tight connection between both approaches. Last, we give some insights and final remarks on this subject.