Communication
Version 1
Preserved in Portico This version is not peer-reviewed
On the Optimal Point of the Weighted Simpson Index
Version 1
: Received: 27 December 2023 / Approved: 28 December 2023 / Online: 28 December 2023 (03:48:05 CET)
A peer-reviewed article of this Preprint also exists.
Casquilho, J.P.; Mena-Matos, H. On the Optimal Point of the Weighted Simpson Index. Mathematics 2024, 12, 507. Casquilho, J.P.; Mena-Matos, H. On the Optimal Point of the Weighted Simpson Index. Mathematics 2024, 12, 507.
Abstract
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.
Keywords
Weighted Simpson index; Lagrange multiplier method; Critical point; Minimum value; Harmonic mean; Inversion problem
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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