The Lognormal Distribution Is Characterized by Its Integer Moments
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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-12-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/12/23/3830 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850107139965583360 |
|---|---|
| author | Pier Luigi Novi Inverardi Aldo Tagliani |
| author_facet | Pier Luigi Novi Inverardi Aldo Tagliani |
| author_sort | Pier Luigi Novi Inverardi |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-06cc26c32e554a3292ab2e4adb3a7e8e |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-06cc26c32e554a3292ab2e4adb3a7e8e2025-08-20T02:38:39ZengMDPI AGMathematics2227-73902024-12-011223383010.3390/math12233830The Lognormal Distribution Is Characterized by Its Integer MomentsPier Luigi Novi Inverardi0Aldo Tagliani1Department of Economics and Management, University of Trento, 38122 Trento, ItalyDepartment of Economics and Management, University of Trento, 38122 Trento, ItalyThe 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.https://www.mdpi.com/2227-7390/12/23/3830differential entropyfractional momentslognormal distributionmaximum entropyindeterminate stieltjes moment problem |
| spellingShingle | Pier Luigi Novi Inverardi Aldo Tagliani The Lognormal Distribution Is Characterized by Its Integer Moments Mathematics differential entropy fractional moments lognormal distribution maximum entropy indeterminate stieltjes moment problem |
| title | The Lognormal Distribution Is Characterized by Its Integer Moments |
| title_full | The Lognormal Distribution Is Characterized by Its Integer Moments |
| title_fullStr | The Lognormal Distribution Is Characterized by Its Integer Moments |
| title_full_unstemmed | The Lognormal Distribution Is Characterized by Its Integer Moments |
| title_short | The Lognormal Distribution Is Characterized by Its Integer Moments |
| title_sort | lognormal distribution is characterized by its integer moments |
| topic | differential entropy fractional moments lognormal distribution maximum entropy indeterminate stieltjes moment problem |
| url | https://www.mdpi.com/2227-7390/12/23/3830 |
| work_keys_str_mv | AT pierluiginoviinverardi thelognormaldistributionischaracterizedbyitsintegermoments AT aldotagliani thelognormaldistributionischaracterizedbyitsintegermoments AT pierluiginoviinverardi lognormaldistributionischaracterizedbyitsintegermoments AT aldotagliani lognormaldistributionischaracterizedbyitsintegermoments |