We propose a new L²‐type goodness‐of‐fit test for the family of beta distributions based on a conditional moment characterization. The asymptotic null distribution is identified, and since it depends on the underlying parameters, a parametric bootstrap procedure is proposed. Consistency against all alternatives that satisfy a convergence criterion is shown, and a Monte Carlo simulation study indicates that the new procedure outperforms most of the classical tests. Finally, the procedure is applied to a real data set related to air humidity.

中文翻译：

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在适合Beta分布的新测试中

我们基于条件矩刻画为贝塔分布族提出了一种新的L ²型拟合优度检验。确定了渐近零分布，并且由于它取决于基础参数，因此提出了参数自举程序。显示了满足收敛标准的所有备选方案的一致性，并且蒙特卡罗模拟研究表明，新程序的性能优于大多数经典测试。最后，将该程序应用于与空气湿度有关的真实数据集。