Exact Distribution of Random Order Statistics and Applications in Risk Management
Exact Distribution of Random Order Statistics and Applications in Risk Management
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随机顺序统计量的精确分布及其在风险管理中的应用
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
M. Koutras
中科院分区：
文献类型：
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作者：
Vasileios M. Koutras;M. Koutras
本文研究了随机变量（r. v.'）样本的顺序统计量的精确分布。s），随机样本量。对于样本的第r个最大观测值的精确分布，给出了一些新的结果，并且当样本大小属于广泛的离散分布类，如幂级数分布族、Panjer分布族、可交换Bernoulli混合分布族和Phase-Type分布族时，得到了一些有趣的性质.最后，我们说明了如何研究中的随机模型可以利用金融风险管理（监测不良贷款和保险投资组合监督）中出现的建模问题。
In the present work we study the exact distribution of order statistics coming from a sample of random variables (r.v.’s), with random sample size. Some new results are provided for the exact distribution of the r −th largest observation of the sample, and several interesting properties are developed when the sample size belongs to wide classes of discrete distributions such as the family of power series distributions, the Panjer Family, the class of exchangeable Bernoulli mixtures and the family of Phase-Type distributions. Finally, we illustrate how the stochastic model under study could be exploited for modeling problems arising in financial risk management (monitoring of non-performing loans and insurance portfolio surveillance).