Asymptotics for ratios with applications to reinsurance

S.A. Ladoucette; J.L. Teugels

doi:10.1007/s11009-007-9020-z

Asymptotics for ratios with applications to reinsurance

S.A. Ladoucette, J.L. Teugels

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Abstract

This paper provides an overview of results pertaining to moment convergence for certain ratios of random variables involving sums, order statistics and extreme terms in the sense of modulus. Most of the literature on this matter originates from Darling (1952) who gave a criterion for the convergence in probability to 1 of the ratio of the maximum to the sum in case of nonnegative random variables.

Original language	English
Pages (from-to)	225-242
Journal	Methodology and Computing in Applied Probability
Volume	9
Issue number	2
DOIs	https://doi.org/10.1007/s11009-007-9020-z
Publication status	Published - 2007

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abstract = "This paper provides an overview of results pertaining to moment convergence for certain ratios of random variables involving sums, order statistics and extreme terms in the sense of modulus. Most of the literature on this matter originates from Darling (1952) who gave a criterion for the convergence in probability to 1 of the ratio of the maximum to the sum in case of nonnegative random variables.",

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AB - This paper provides an overview of results pertaining to moment convergence for certain ratios of random variables involving sums, order statistics and extreme terms in the sense of modulus. Most of the literature on this matter originates from Darling (1952) who gave a criterion for the convergence in probability to 1 of the ratio of the maximum to the sum in case of nonnegative random variables.

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DO - 10.1007/s11009-007-9020-z

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JO - Methodology and Computing in Applied Probability

JF - Methodology and Computing in Applied Probability

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ER -

Asymptotics for ratios with applications to reinsurance

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