The Lognormal Distribution Is Characterized by Its Integer Moments

Pier Luigi Novi Inverardi () and Aldo Tagliani
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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

Mathematics, 2024, vol. 12, issue 23, 1-11

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.

Keywords: differential entropy; fractional moments; lognormal distribution; maximum entropy; indeterminate stieltjes moment problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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