Heavy-tailed distributions, such as the Cauchy distribution, are acknowledged for providing more accurate models for financial returns, as the normal distribution is deemed insufficient for capturing the significant fluctuations observed in real-world assets. Data sets characterized by outlier sensitivity are critically important in diverse areas, including finance, economics, telecommunications, and signal processing. This article addresses a goodness-of-fit test for the Cauchy distribution. The proposed test utilizes empirical likelihood methods, including the jackknife empirical likelihood (JEL) and adjusted jackknife empirical likelihood (AJEL). Extensive Monte Carlo simulation studies are conducted to evaluate the finite sample performance of the proposed test. The application of the proposed test is illustrated through the analysing two real data sets.

翻译：重尾分布（如柯西分布）被公认为能更准确地建模金融收益率，因为正态分布被认为不足以捕捉现实资产中观察到的剧烈波动。对异常值敏感的数据集在金融、经济、电信和信号处理等多个领域至关重要。本文针对柯西分布的拟合优度检验展开研究。所提出的检验方法采用经验似然法，包括刀切经验似然（JEL）和调整刀切经验似然（AJEL）。通过大量的蒙特卡洛模拟研究评估了所提出检验在有限样本下的性能。本文通过分析两个真实数据集展示了所提出检验的应用。