We deal with absolutely continuous probability distributions with finite all-positive integer-order moments. It is well known that any such distribution is either uniquely determined by its moments (M-determinate), or it is non-unique (M-indeterminate). In this paper, we follow the maximum entropy approach and establish a new criterion for the M-indeterminacy of distributions on the positive half-line (Stieltjes case). Useful corollaries are derived for M-indeterminate distributions on the whole real line (Hamburger case). We show how the maximum entropy is related to the symmetry property and the M-indeterminacy.

Maximum Entropy Criterion for Moment Indeterminacy of Probability Densities / Stoyanov, Jordan M.; Tagliani, Aldo; Novi Inverardi, Pier Luigi. - In: ENTROPY. - ISSN 1099-4300. - ELETTRONICO. - 26:2(2024), p. e26020121. [10.3390/e26020121]

Maximum Entropy Criterion for Moment Indeterminacy of Probability Densities

Tagliani, Aldo
Secondo
;
Novi Inverardi, Pier Luigi
Ultimo
2024-01-01

Abstract

We deal with absolutely continuous probability distributions with finite all-positive integer-order moments. It is well known that any such distribution is either uniquely determined by its moments (M-determinate), or it is non-unique (M-indeterminate). In this paper, we follow the maximum entropy approach and establish a new criterion for the M-indeterminacy of distributions on the positive half-line (Stieltjes case). Useful corollaries are derived for M-indeterminate distributions on the whole real line (Hamburger case). We show how the maximum entropy is related to the symmetry property and the M-indeterminacy.
2024
2
Stoyanov, Jordan M.; Tagliani, Aldo; Novi Inverardi, Pier Luigi
Maximum Entropy Criterion for Moment Indeterminacy of Probability Densities / Stoyanov, Jordan M.; Tagliani, Aldo; Novi Inverardi, Pier Luigi. - In: ENTROPY. - ISSN 1099-4300. - ELETTRONICO. - 26:2(2024), p. e26020121. [10.3390/e26020121]
File in questo prodotto:
File Dimensione Formato  
Entropy-26-00121.pdf

accesso aperto

Tipologia: Versione editoriale (Publisher’s layout)
Licenza: Creative commons
Dimensione 273.07 kB
Formato Adobe PDF
273.07 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/401689
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact