GENERALIZING THE LOG-MOYAL DISTRIBUTION AND REGRESSION MODELS FOR HEAVY-TAILED LOSS DATA
GENERALIZING THE LOG-MOYAL DISTRIBUTION AND REGRESSION MODELS FOR HEAVY-TAILED LOSS DATA
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重尾损失数据的 Log-Moyal 分布和回归模型的推广
DOI：
10.1002/admt.201901007
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发表时间：
2021-01-01
期刊：
影响因子：
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通讯作者：
Meng, Shengwang
中科院分区：
文献类型：
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作者：
Li, Zhengxiao;Beirlant, Jan;Meng, Shengwang
灾难性损失数据具有厚尾性。然后，从业者需要能够捕获索赔数据的尾部和模态部分的模型。为此，提出了一个新的参数损失分布族，作为Bhati和Ravi（2018）的广义log-Moyal分布的伽玛混合，称为广义log-Moyal伽玛（GLMGA）分布。虽然GLMGA分布是GB 2分布的一个特例，但我们证明了这种更简单的模型在大型和模态损耗数据的回归建模中是有效的。通过对中国地震损失数据集的详细分析，与文献中的竞争模型的结果进行比较，说明了回归建模及其在风险度量中的应用。为此，我们讨论的概率特性的GLMGA和统计估计的参数，通过最大似然。康明斯等人（1990）报告的火灾索赔数据集以及Bhati和Ravi（2018）最近讨论的挪威火灾损失数据集进一步说明了新一类分布的适用性。
Catastrophic loss data are known to be heavy-tailed. Practitioners then need models that are able to capture both tail and modal parts of claim data. To this purpose, a new parametric family of loss distributions is proposed as a gamma mixture of the generalized log-Moyal distribution from Bhati and Ravi (2018), termed the generalized log-Moyal gamma (GLMGA) distribution. While the GLMGA distribution is a special case of the GB2 distribution, we show that this simpler model is effective in regression modeling of large and modal loss data. Regression modeling and applications to risk measurement are illustrated using a detailed analysis of a Chinese earthquake loss data set, comparing with the results of competing models from the literature. To this end, we discuss the probabilistic characteristics of the GLMGA and statistical estimation of the parameters through maximum likelihood. Further illustrations of the applicability of the new class of distributions are provided with the fire claim data set reported in Cummins et al. (1990) and a Norwegian fire losses data set discussed recently in Bhati and Ravi (2018).