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On the Optimal Point of the Weighted Simpson Index

Author

Listed:
  • 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)

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.

Suggested Citation

  • José Pinto Casquilho & Helena Mena-Matos, 2024. "On the Optimal Point of the Weighted Simpson Index," Mathematics, MDPI, vol. 12(4), pages 1-7, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:4:p:507-:d:1334646
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    References listed on IDEAS

    as
    1. Kasulo, Victor & Perrings, Charles, 2006. "Fishing down the value chain: Biodiversity and access regimes in freshwater fisheries -- the case of Malawi," Ecological Economics, Elsevier, vol. 59(1), pages 106-114, August.
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