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The Lognormal Distribution Is Characterized by Its Integer Moments

Author

Listed:
  • Pier Luigi Novi Inverardi

    (Department of Economics and Management, University of Trento, 38122 Trento, Italy)

  • Aldo Tagliani

    (Department of Economics and Management, University of Trento, 38122 Trento, Italy)

Abstract

The lognormal moment sequence is considered. Using the fractional moments technique, it is first proved that the lognormal has the largest differential entropy among the infinite positively supported probability densities with the same lognormal-moments. Then, relying on previous theoretical results on entropy convergence obtained by the authors concerning the indeterminate Stieltjes moment problem, the lognormal distribution is accurately reconstructed by the maximum entropy technique using only its integer moment sequence, although it is not uniquely determined by moments.

Suggested Citation

  • Pier Luigi Novi Inverardi & Aldo Tagliani, 2024. "The Lognormal Distribution Is Characterized by Its Integer Moments," Mathematics, MDPI, vol. 12(23), pages 1-11, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3830-:d:1536323
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    References listed on IDEAS

    as
    1. Novi Inverardi, Pier Luigi & Tagliani, Aldo & Milev, Mariyan, 2024. "Indeterminate Hamburger moment problem: Entropy convergence," Statistics & Probability Letters, Elsevier, vol. 212(C).
    2. Luca Bagnato & Antonio Punzo, 2013. "Finite mixtures of unimodal beta and gamma densities and the $$k$$ -bumps algorithm," Computational Statistics, Springer, vol. 28(4), pages 1571-1597, August.
    3. Punzo, Antonio & Bagnato, Luca & Maruotti, Antonello, 2018. "Compound unimodal distributions for insurance losses," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 95-107.
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