Delicate Comparison of the Central and Non-Central Lyapunov Ratios with Applications to the Berry–Esseen Inequality for Compound Poisson Distributions
Abstract
:1. Introduction
2. Formulations of Main Results
3. Reduction to the Case of Two-Point Distributions
- it is a linear combination , of the functions generating the given moment conditions ; and
- it has exactly two tangent points with .
4. Analysis of Two-Point Distributions
5. Proofs of Main Results
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
i.i.d. | independent and identically distributed |
r.v. | random variable |
iff | if and only if |
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Makarenko, V.; Shevtsova, I. Delicate Comparison of the Central and Non-Central Lyapunov Ratios with Applications to the Berry–Esseen Inequality for Compound Poisson Distributions. Mathematics 2023, 11, 625. https://doi.org/10.3390/math11030625
Makarenko V, Shevtsova I. Delicate Comparison of the Central and Non-Central Lyapunov Ratios with Applications to the Berry–Esseen Inequality for Compound Poisson Distributions. Mathematics. 2023; 11(3):625. https://doi.org/10.3390/math11030625
Chicago/Turabian StyleMakarenko, Vladimir, and Irina Shevtsova. 2023. "Delicate Comparison of the Central and Non-Central Lyapunov Ratios with Applications to the Berry–Esseen Inequality for Compound Poisson Distributions" Mathematics 11, no. 3: 625. https://doi.org/10.3390/math11030625
APA StyleMakarenko, V., & Shevtsova, I. (2023). Delicate Comparison of the Central and Non-Central Lyapunov Ratios with Applications to the Berry–Esseen Inequality for Compound Poisson Distributions. Mathematics, 11(3), 625. https://doi.org/10.3390/math11030625