Entropies of Sums of Independent Gamma Random Variables

Entropies of Sums of Independent Gamma Random Variables

We establish several Schur-convexity type results under fixed variance for weighted sums of independent gamma random variables and obtain nonasymptotic bounds on their Rényi entropies. In particular, this pertains to the recent results by Bartczak–Nayar–Zwara as well as Bobkov–Naumov–Ulyanov, offeri...

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Veröffentlicht in:Journal of theoretical probability 2023-06, Vol.36 (2), p.1227-1242
Hauptverfasser: Chasapis, Giorgos, Singh, Salil, Tkocz, Tomasz
Format: Artikel
Sprache:eng
Schlagworte:
Convexity
Entropy (Information theory)
Independent variables
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Random variables
Statistics
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Zusammenfassung:We establish several Schur-convexity type results under fixed variance for weighted sums of independent gamma random variables and obtain nonasymptotic bounds on their Rényi entropies. In particular, this pertains to the recent results by Bartczak–Nayar–Zwara as well as Bobkov–Naumov–Ulyanov, offering simple proofs of the former and extending the latter.
ISSN:0894-9840
1572-9230
DOI:10.1007/s10959-022-01192-y