数学
拟合优度
幂律
泊松分布
分布(数学)
应用数学
估计理论
指数
区间估计
帕累托分布
统计的
经验分布函数
功率(物理)
统计
法学
统计物理学
数学分析
置信区间
物理
量子力学
政治学
哲学
语言学
标识
DOI:10.1016/j.physa.2024.129695
摘要
For discrete segmental power-law distributions, the probability ratio ft/ft+1 is a linear function of the exponent parameter. Based on this property, the estimation of the exponent parameter and a goodness-of-fit testing method are provided. The proposed testing method is parameter-independent and the testing statistic is proved to asymptotically follow a chi-square distribution. In the region where power-law properties exist, the testing method and the estimation method can be applied by segments, so they can also be used to determine interval endpoints. These methods can also be extended to other discrete distributions such as Yule distribution, Poisson distribution, Geometry distribution and so on. Some simulation results of synthetic truncated power-law distributions provide support for the effectiveness of the proposed methods. To demonstrate the applicability of the method, two empirical examples, word frequencies of the novel Moby Dick and US casuality numbers in the American Indian War, are analyzed.
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