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.
The Lognormal Distribution Is Characterized by Its Integer Moments / Novi Inverardi, Pier Luigi; Tagliani, Aldo. - In: MATHEMATICS. - ISSN 2227-7390. - ELETTRONICO. - 12:23(2024). [10.3390/math12233830]
The Lognormal Distribution Is Characterized by Its Integer Moments
Novi Inverardi, Pier Luigi
Primo
;Tagliani, AldoUltimo
2024-01-01
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.File | Dimensione | Formato | |
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