The Kolmogorov-Smirnov (KS) test is popularly used in many applications, such as anomaly detection, astronomy, database security and AI systems. One challenge remained untouched how we can obtain an explanation on why a set fails the KS test. In this paper, tackle problem of producing counterfactual explanations for data failing Concept-wise, propose notion most comprehensible explanations, whi...

Smirnov domains with non-smooth boundaries do admit non-trivial functions of Smirnov class with real boundary values. We will show that the existance of functions in Smirnov classes with real boundary values is directly dependent on the boundary characteristics of a Smirnov domain. Mathematics Subject Classification (2000). 30H10, 30H15.

In this paper, we are interested in extending the classical KolmogorovSmirnov homogeneity test to compare two samples of interval-valued observed measurements. In such a case, the test result is interval-valued, and one major difficulty is to find the bounds of this set. We propose a very efficient computational method for approximating these bounds by using a p-box (pairs of upper and lower cu...

When a reliability analysis, survival analysis, or discrete-event simulation input modeling analysis is performed, it is typically the case that a modeler collects data associated with some system under consideration. Although this raw data provides an initial insight into the stochastic elements of the system, often it is desirable to construct a model of the system which is tractable for math...

We prove the following conjecture of Narayana: there are no nontrivial dominance refinements of the Smirnov two-sample test if and only if the two sample sizes are relatively prime. We also count the number of natural significance levels of the Smirnov two-sample test in terms of the sample sizes and relate this to the Narayana conjecture. In particular, Smirnov tests with relatively prime samp...

Based on the γ-ray data of blazars in the third EGRET catalog and radio data at 5 GHz, we studied the correlation between the radio and γ-ray luminosities using two statistical methods. The first method was the partial correlation analysis method, which indicates that there exist correlations between the radio and γ-ray luminosities in both high and low states as well as in the average case. Th...