We propose tests of fit for classes of distributions that include the Weibull, the Pareto and the Fr\'echet, distributions. The new tests employ the novel tool of the min--characteristic function and are based on an L2--type weighted distance between this function and its empirical counterpart applied on suitably standardized data. If data--standardization is performed using the MLE of the distributional parameters then the method reduces to testing for the standard member of the family, with parameter values known and set equal to one. We investigate asymptotic properties of the tests, while a Monte Carlo study is presented that includes the new procedure as well as competitors for the purpose of specification testing with three extreme value distributions. The new tests are also applied on a few real--data sets.

翻译：本文提出针对威布尔分布、帕累托分布及弗雷歇分布等分布族的拟合优度检验方法。新检验采用最小特征函数这一创新工具，基于该函数与其在适当标准化数据上经验估计量之间的L2型加权距离。若利用分布参数的最大似然估计进行数据标准化，该方法可转化为检验分布族的标准成员，此时参数值已知且设为1。我们研究了检验的渐近性质，并通过蒙特卡洛模拟将新方法与现有方法在三种极值分布的设定检验中进行比较。此外，新方法还被应用于若干真实数据集。