AI 中文总结
本文提出基于记录值的不准确性测度，推导多种寿命分布的显式表达式，开发非参数对称性拟合优度检验，经模拟和实际数据验证，该检验兼具良好的水平维持能力与高功效。
AI 中文摘要
本文研究针对记录值的信息论不准确性测度及其在对称性检验中的应用。我们将Kerridge不准确性测度、累积残差不准确性、累积过去不准确性以及基于extropy的不准确性测度应用于第n个上k-记录值和下k-记录值的分布，针对指数分布、帕累托分布、威布尔分布和均匀分布等多种常见寿命分布推导了显式表达式，并分析了这些测度相对于记录阶数n、参数k及分布参数的单调行为。基于“上记录与下记录不准确性相等意味着分布对称”这一已知特性，我们开发了一种非参数对称性拟合优度检验方法，检验统计量为上记录与下记录估计Kerridge不准确性测度的差值，其零分布通过强制对称性的自助法得到。模拟研究表明，该检验对多种对称分布能维持其名义水平，且对偏态备择假设具有高功效；年最高气温的实际数据示例也证实了其实际应用价值。
英文摘要
This paper studies information-theoretic inaccuracy measures for record values and their application to testing symmetry. We study the Kerridge inaccuracy measure, cumulative residual inaccuracy, cumulative past inaccuracy, and extropy-based inaccuracy measures to the distributions of nth upper and lower k-record values. Explicit expressions are derived for several common lifetime distributions (exponential, Pareto, Weibull, and uniform), and the monotonic behaviour of these measures with respect to the record order n, the parameter k, and the distributional parameters is analysed. Building on the known characterisation that equality of upper and lower record-based inaccuracy implies symmetry, we develop a nonparametric goodness-of-fit test for symmetry. The test statistic is the difference between the estimated Kerridge inaccuracy measures for upper and lower records, and its null distribution is obtained by a bootstrap procedure that enforces symmetry. A simulation study demonstrates that the test maintains its nominal level for a variety of symmetric distributions and achieves high power against skewed alternatives, while a real-data illustration on annual maximum temperatures confirms its practical usefulness.
Comments17 page
