Asymptotic behavior of the ratio of tail probabilities of sum and maximum of independent random variables

DOI10.1007/s10986-012-9153-9zbMath1284.60102OpenAlexW2027386452MaRDI QIDQ392990

Yue-bao Wang, Dong Ya Cheng

Publication date: 15 January 2014

Published in: Lithuanian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10986-012-9153-9

zbMATH Keywords

tail probabilitymaximumlong-tailed distributionsumasymptotic lower and upper boundsO-subexponential distribution

Mathematics Subject Classification ID

Extreme value theory; extremal stochastic processes (60G70) Probability distributions: general theory (60E05) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Limit theorems in probability theory (60F99)

Related Items (4)

A note on product-convolution for generalized subexponential distributions ⋮ On asymptotic equivalence among the solutions of some defective renewal equations ⋮ The local asymptotic estimation for the supremum of a random walk with generalized strong subexponential summands ⋮ Some properties of the exponential distribution class with applications to risk theory

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• Some closure properties for subexponential distributions
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• Infinite divisibility and generalized subexponentiality
• On the non-closure under convolution of the subexponential family
• Convolution equivalence and infinite divisibility

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