On the Optimal Point of the Weighted Simpson Index

José Pinto Casquilho () and Helena Mena-Matos ()
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José Pinto Casquilho: Postgraduate and Research Program, Universidade Nacional Timor Lorosa’e (UNTL), Díli, Timor-Leste
Helena Mena-Matos: Centro de Matemática da Universidade do Porto (CMUP), Faculdade de Ciências da Universidade do Porto (FCUP), 4169-007 Porto, Portugal

Mathematics, 2024, vol. 12, issue 4, 1-7

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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