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- W2551003075 abstract "The Berry–Esseen (BE) theorem of probability theory is employed to establish bounds on percentile estimates for compound-Poisson loss portfolios. We begin by arguing that these bounds should not be based upon the exact BE constant, but rather upon a possibly lower, asymptotic counterpart for which the Lyapunov fraction converges uniformly to zero. We use this constant to construct two bounds – one approximate, and the other exact – and then propose a simple numerical criterion for determining whether the Gaussian approximation affords sufficient accuracy for a given Poisson mean and individual-loss distribution. Applying this criterion to the cases of gamma and lognormal individual losses, we find there exists a positive lower bound for the minimum Poisson mean necessary to achieve a fixed degree of accuracy for losses generated by the ‘best-case’ individual-loss distribution. Further investigation of this ‘best case’ reveals that large minimum Poisson means (i.e. 700) are required to achieve reasonable a..." @default.
- W2551003075 created "2016-11-30" @default.
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- W2551003075 date "2016-06-02" @default.
- W2551003075 modified "2023-10-14" @default.
- W2551003075 title "Berry-Esseen bounds for compound-Poisson loss percentiles" @default.
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- W2551003075 doi "https://doi.org/10.1080/03461238.2016.1182064" @default.
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