The Power of Alternative Kolmogorov-Smirnov Tests Based on Transformations of the Data

摘要: The Kolmogorov-Smirnov (KS) statistical test is commonly used to determine if data can be regarded as a sample from sequence of independent and identically distributed (i.i.d.) random variables with specified continuous cumulative distribution function (cdf) F, but small samples it have insufficient power, that is, its probability rejecting natural alternatives too low. However, in 1961, Durbin showed the power KS often increased, for given significance level, by well-chosen transformation data. Simulation experiments reported here show more consistently substantially increased different transformation. We first transform mean-1 exponential variables, which equivalent rate-1 Poisson process. then apply classical conditional-uniform convert arrival times into i.i.d. uniformly on [0, 1]. And then, after those two preliminary steps, we original Since these tests assume fully cdf, also investigate consequence having estimate parameters cdf.