Related papers: A New ECDF Two-Sample Test Statistic
The two-sample Kolmogorov-Smirnov test is a widely used statistical test for detecting whether two samples are likely to come from the same distribution. Implementations typically recur on an article of Hodges from 1957. The advances in…
The cumulative distribution and quantile functions for the two-sided one sample Kolmogorov-Smirnov probability distributions are used for goodness-of-fit testing. The CDF is notoriously difficult to explicitly describe and to compute, and…
Classical tests are available for the two-sample test of correspondence of distribution functions. From these, the Kolmogorov-Smirnov test provides also the graphical interpretation of the test results, in different forms. Here, we propose…
In recent years, Bayesian nonparametric statistics has gathered extraordinary attention. Nonetheless, a relatively little amount of work has been expended on Bayesian nonparametric hypothesis testing. In this paper, a novel Bayesian…
The cumulative distribution and quantile functions for the one-sided one sample Kolmogorov-Smirnov probability distributions are used for goodness-of-fit testing. While the Smirnov-Birnbaum-Tingey formula for the CDF appears straight…
The classical two-sample test of Kolmogorov-Smirnov (KS) is widely used to test whether empirical samples come from the same distribution. Even though most statistical packages provide an implementation, carrying out the test in big data…
This paper considers the problem of testing the equality of two unspecified distributions. The classical omnibus tests such as the Kolmogorov-Smirnov and Cram\`er-von Mises are known to suffer from low power against essentially all but…
To establish the electron energy distribution function (EEDF), the second derivative of a Langmuir probe current-voltage (I-V) characteristic is numerically integrated using the Tikhonov singular value decomposition regularized method. A…
We present the results of a large number of simulation studies regarding the power of various non-parametric two-sample tests for multivariate data. This includes both continuous and discrete data. In general no single method can be relied…
Goodness-of-fit tests gauge whether a given set of observations is consistent (up to expected random fluctuations) with arising as independent and identically distributed (i.i.d.) draws from a user-specified probability distribution known…
We review a finite-sampling exponential bound due to Serfling and discuss related exponential bounds for the hypergeometric distribution. We then discuss how such bounds motivate some new results for two-sample empirical processes. Our…
When comparing two distributions, it is often helpful to learn at which quantiles or values there is a statistically significant difference. This provides more information than the binary "reject" or "do not reject" decision of a global…
Statistical distances quantifies the difference between two statistical constructs. In this article, we describe reference values for a distance between samples derived from the Kolmogorov-Smirnov statistic $D_{F,F'}$. Each measure of the…
Consider $n$ iid random variables, where $\xi_1, \ldots, \xi_n$ are $n$ realisations of a random variable $\xi$ and $\zeta_1, \ldots, \zeta_n$ are $n$ realisations of a random variable $\zeta$. The distribution of each realisation of $\xi$,…
We present the results of a large number of simulation studies regarding the power of various goodness-of-fit as well as nonparametric two-sample tests for univariate data. This includes both continuous and discrete data. In general no…
We introduce a powerful deep classifier two-sample test for high-dimensional data based on E-values, called E-value Classifier Two-Sample Test (E-C2ST). Our test combines ideas from existing work on split likelihood ratio tests and…
We analyzed the effect of the deviation of the exact distribution of the p-values from the uniform distribution on the Kolmogorov-Smirnov (K-S) test that was implemented as the second-level randomness test. We derived an inequality that…
We present the results of a large number of simulation studies regarding the power of various goodness-of-fit as well as non-parametric two-sample tests for multivariate data. In two dimensions this includes both continuous and discrete…
This paper introduces a novel two-sample test for a broad class of orthogonally equivalent positive definite symmetric matrix distributions. Our test is the first of its kind and we derive its asymptotic distribution. To estimate the test…
New goodness-of-fit tests for exponentiality based on a particular property of exponential law are constructed. Test statistics are functionals of U-empirical processes. The first of these statistics is of integral type, the second one is a…