7 The nonparametric minimum hypergeometric (mHG) test is a popular alternative to Kolmogorov-Smirnov (KS)-type tests for determining gene set enrichment. However, these approaches have not been compared to each other in a quantitative manner. Here, I first perform a simulation study to show that the mHG test is significantly more powerful than the one-sided KS test for detecting gene set enrich...

A theme of recent side-channel research has been the quest for distinguishers which remain e ective even when few assumptions can be made about the underlying distribution of the measured leakage traces. The Kolmogorov-Smirnov (KS) test is a well known nonparametric method for distinguishing between distributions, and, as such, a perfect candidate and an interesting competitor to the (already m...

We present a systematic study of the dynamical scaling process leading to the establishment of the Kolmogorov-Zakharov (KZ) spectrum in weak three-wave turbulence. In the finite-capacity case, in which the transient spectrum reaches infinite frequency in finite time, the dynamical scaling exponent is anomalous in the sense that it cannot be determined from dimensional considerations. As a conse...

The importance of normal distribution is undeniable since it is an underlying assumption of many statistical procedures such as t-tests, linear regression analysis, discriminant analysis and Analysis of Variance (ANOVA). When the normality assumption is violated, interpretation and inferences may not be reliable or valid. The three common procedures in assessing whether a random sample of indep...

The OGLE data for Einstein ring crossing times, tE, for microlensing events toward the galactic bulge are analyzed. The analysis shows that the crossing times are bimodal, indicating that two populations of lenses could be responsible for observed microlensing events. Given the possibility that microlensing in this direction can be due to both main-sequence stars and white dwarfs, we analyze an...

The Kolmogorov-Smirnov (KS) statistical test is commonly used to determine if data can be regarded as a sample from a sequence of i.i.d. random variables with specified continuous cdf F , but with small samples it can have insufficient power, i.e., its probability of rejecting natural alternatives can be too low. However, Durbin [1961] showed that the power of the KS test often can be increased...

The statistical properties of the return intervals τq between successive 1-min volatilities of 30 liquid Chinese stocks exceeding a certain threshold q are carefully studied. The Kolmogorov-Smirnov (KS) test shows that 12 stocks exhibit scaling behaviors in the distributions of τq for different thresholds q. Furthermore, the KS test and weighted KS test shows that the scaled return interval dis...

8 The XL-mHG test is a semiparametric test for enrichment in ranked lists with boolean (0/1-valued) entries. It is a generalization of the nonparametric mHG test, designed to provide some control over the kind of enrichment that is being tested for, and to allow a flexible trade-off between the sensitivity and robustness of the test. Here, I describe an improved algorithm to efficiently calcula...

This study aims to compare normality tests in different sample sizes data with normal distribution under kurtosis and skewness coefficients obtained simulatively. To this end, firstly, simulative were produced using the MATLAB program for skewness/kurtosis sizes. The analysis of each type was conducted ten tests; namely, (Kolmogorov Smirnov (KS) Test, KS Stephens Modification, Marsaglia, Lillie...

This paper introduces a complement statistical test for distinguishing between the predictive accuracy of two sets of forecasts. We propose a non-parametric test founded upon the principles of the Kolmogorov-Smirnov (KS) test, referred to as the KS Predictive Accuracy (KSPA) test. The KSPA test is able to serve two distinct purposes. Initially, the test seeks to determine whether there exists a...