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Entropies of Sums of Independent Gamma Random Variables

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Abstract

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.

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Acknowledgements

We are indebted to Han Nguyen for many fruitful and illuminating discussions. We should like to thank an anonymous referee very much for their insightful comments greatly improving this manuscript.

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Correspondence to Giorgos Chasapis.

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TT’s research supported in part by NSF grant DMS-1955175.

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Chasapis, G., Singh, S. & Tkocz, T. Entropies of Sums of Independent Gamma Random Variables. J Theor Probab 36, 1227–1242 (2023). https://doi.org/10.1007/s10959-022-01192-y

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