Goodness-of-fit test using the ratio of truncated moments for a subexponential distribution

This paper presents a novel goodness-of-fit (GoF) test, based on the ratio of truncated moments, designed for a broad class of probability models. While the test is applicable to general distributions, we demonstrate its utility by applying it to the newly developed Double Odds Geometric Power (DOGP) distribution, a flexible heavy-tailed model. The DOGP distribution is motivated by the observation that simple transformations of the power-function distribution often yield well-known heavy-tailed families; building on this idea, we construct the DOGP as a new transformation of a generalized power-function distribution, extending its tail flexibility and modeling capabilities. The GoF test is derived using U-statistic theory, its asymptotic properties are established, and its performance is examined through extensive Monte Carlo simulations. Parameter estimation for the DOGP model is carried out using the maximum likelihood method, and both the model and the GoF test are applied to simulated data and three real-world datasets, illustrating their accuracy and practical relevance.