Journal ArticleDOI
On sufficient conditions for the comparison in the excess wealth order and spacings
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TLDR
Sufficient conditions for the excess wealth order are provided based on properties of the quantile functions which are useful when the dispersive order does not hold and it is shown how these results can provide comparisons of quantities of interest in reliability and insurance.Abstract:
The purpose of this paper is twofold. On the one hand, we provide sufficient conditions for the excess wealth order. These conditions are based on properties of the quantile functions which are useful when the dispersive order does not hold. On the other hand, we study sufficient conditions for the comparison in the increasing convex order of spacings of generalized order statistics. These results will be combined to show how we can provide comparisons of quantities of interest in reliability and insurance.read more
Citations
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Stochastic orders and co-risk measures under positive dependence
TL;DR: In this paper, the authors provide sufficient conditions under which two random vectors could be compared in terms of CoVaR (conditional value-at-risk), CoES (Conditional expected shortfall) and different risk contribution measures.
Journal ArticleDOI
Stochastic comparisons of interfailure times under a relevation replacement policy
TL;DR: Comparisons of the failure times and interfailure times of two systems based on a replacement policy proposed by Kapodistria and Psarrakos (2012) are provided and it is shown that when the first failure times are ordered in terms of the dispersive order, then the successive interfailur times are orders in the usual stochastic order.
Journal ArticleDOI
On the Comparison of Relative Spacings with Applications
TL;DR: In this article, the authors introduce the notion of relative spacings, and provide several results for the comparison of relative spaces between two populations, including reliability and economy, and show the interest of this notion in several contexts.
Journal ArticleDOI
On a family of risk measures based on largest claims
TL;DR: In this paper, the expected average of the n − i largest claims, with 0 ≤ i ≤ n − 1, is shown to be a distortion risk measure with concave distortion function that can be represented in terms of mixtures of tail value-at-risks with beta mixing distributions.
Journal ArticleDOI
On sufficient conditions for the comparison of some quantile-based measures
TL;DR: In this article, the authors focus on characterizations and sufficient conditions for the comparison of some quantile-based measures, mainly focusing on crossing conditions and changes of monotonicity of the quantile functions.
References
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Journal ArticleDOI
Statistical Theory of Reliability and Life Testing Probability Models
Book
Statistical Theory of Reliability and Life Testing: Probability Models
Richard E. Barlow,Frank Proschan +1 more
TL;DR: A number of new classes of life distributions arising naturally in reliability models are treated systematically and each provides a realistic probabilistic description of a physical property occurring in the reliability context, thus permitting more realistic modeling of commonly occurring reliability situations.
Book
Modelling Extremal Events: for Insurance and Finance
TL;DR: In this article, an approach to Extremes via Point Processes is presented, and statistical methods for Extremal Events are presented. But the approach is limited to time series analysis for heavy-tailed processes.
Journal ArticleDOI
Modelling Extremal Events for Insurance and Finance
TL;DR: In this article, Modelling Extremal Events for Insurance and Finance is discussed. But the authors focus on the modeling of extreme events for insurance and finance, and do not consider the effects of cyber-attacks.