Goodness-of-Fit Test Based on the Ratio of Truncated Moments

We propose a new goodness-of-fit (GoF) test for distributions defined on the unit interval, constructed using the ratio of truncated moments. The test statistic is developed within the framework of U-statistics, and its asymptotic properties are rigorously established. The empirical performance of the test is evaluated through extensive Monte Carlo simulations under various alternatives, demonstrating strong power across a range of scenarios. To illustrate the utility of the proposed GoF test, we introduce a novel unit interval distribution, termed the Generalized Yun (GY) distribution, which exhibits unimodality, an increasing failure rate, and geometric extreme stability. Applications to three real-world datasets further underscore the practical relevance of the test.