A new goodness-of-fit version of the Girone-Cifarelli test

The classical goodness-of-fit problem, in the case of a null continuous and completely specified distribution, is faced by a new version of the Girone-Cifarelli test. This latter test was introduced for the two-sample problem and showed a substantial gain of power over other common tests based on the empirical distribution function, like the Kolmogorov-Smirnov test. After considering the problem of the definition of the test-statistic in the goodness-of-fit framework, this paper deals with the sample properties of the test and compares it with its classical competitors. The superiority of the Girone-Cifarelli test is shown via a simulation study considering symmetric and skewed distributions.