基于平均剩余寿命表征的帕累托I型分布拟合优度检验
Goodness-of-fit testing for the Pareto type-I distribution based on a mean residual life characterization
- Indian Institute of Technology Tirupati（蒂鲁帕蒂印度理工学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对帕累托I型分布，基于平均剩余寿命表征提出新型拟合优度检验，通过U统计量构建统计量，模拟显示其控制显著性水平且功效具竞争力，并用实际数据集验证。
AI中文摘要：
重尾数据的统计分析已受到大量关注，因为极端观测值频繁出现在许多实际应用中。帕累托I型分布是经济学、金融学、精算科学、保险学、可靠性分析和极值分析中使用的基础重尾模型。本文中，我们利用平均剩余寿命表征提出了针对帕累托分布的新型拟合优度检验。检验统计量通过U统计量理论构建，在原假设和备择假设下均确立了其渐近性质。通过蒙特卡洛模拟，采用最大似然估计和矩估计评估其有限样本性能，并与现有检验进行比较。结果表明，所提出的检验能控制名义显著性水平，且在广泛的备择假设下具有竞争力的功效。最后，利用丹麦火灾保险损失数据集和污染数据集对所提方法进行了说明。
英文摘要：
The statistical analysis of heavy-tailed data has received considerable attention because extreme observations frequently arise in many practical applications. The Pareto type-I distribution is a fundamental heavy-tailed model used in economics, finance, actuarial science, insurance, reliability, and extreme value analysis. In this paper, we propose novel goodness-of-fit tests for the Pareto distribution using a mean residual life characterization. The test statistic is constructed using U-statistic theory, and its asymptotic behaviour is established under both the null and alternative hypotheses. Its finite-sample performance is evaluated through Monte Carlo simulations using maximum-likelihood and method-of-moments estimation and compared with existing tests. The results show that the proposed test controls the nominal significance level and performs competitively in terms of power across a broad range of alternatives. Finally, the proposed methodology is illustrated using the Danish fire insurance loss and pollution datasets.
