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We introduce a new statistical quantity the energy to test whether two samples originate from the same distributions. The energy is a simple logarithmic function of the distances of the observations in the variate space. The distribution of…
Over the past decades, various methods for comparing the means of two log-normal have been proposed. Some of them are differing in terms of how the statistic test adjust to accept or to reject the null hypothesis. In this study, a new…
Many man-made and natural phenomena, including the intensity of earthquakes, population of cities and size of international wars, are believed to follow power-law distributions. The accurate identification of power-law patterns has…
Searches for unknown physics and decisions between competing astrophysical models to explain data both rely on statistical hypothesis testing. The usual approach in searches for new physical phenomena is based on the statistical Likelihood…
We study a large-scale one-sided multiple testing problem in which test statistics follow normal distributions with unit variance, and the goal is to identify signals with positive mean effects. A conventional approach is to compute…
Multivariate analyses play an important role in high energy physics. Such analyses often involve performing an unbinned maximum likelihood fit of a probability density function (p.d.f.) to the data. This paper explores a variety of unbinned…
Given samples from two non-negative random variables, we propose a family of tests for the null hypothesis that one random variable stochastically dominates the other at the second order. Test statistics are obtained as functionals of the…
Power-law distributions contain precious information about a large variety of processes in geoscience and elsewhere. Although there are sound theoretical grounds for these distributions, the empirical evidence in favor of power laws has…
We propose novel methodology for testing equality of model parameters between two high-dimensional populations. The technique is very general and applicable to a wide range of models. The method is based on sample splitting: the data is…
Many objects studied in astronomy follow a power law distribution function, for example the masses of stars or star clusters. A still used method by which such data is analysed is to generate a histogram and fit a straight line to it. The…
We suggest a method for statistical tests which does not suffer from a posteriori manipulations with tested samples (e.g. cuts optimization) and does not require a somewhat obscure procedure of the penalty estimate. The idea of the method…
We propose a method for setting limits that avoids excluding parameter values for which the sensitivity falls below a specified threshold. These "power-constrained" limits (PCL) address the issue that motivated the widely used CLs…
Despite their importance in supporting experimental conclusions, standard statistical tests are often inadequate for research areas, like the life sciences, where the typical sample size is small and the test assumptions difficult to…
Information in the time distribution of points in a state space reconstructed from observed data yields a test for ``nonstationarity''. Framed in terms of a statistical hypothesis test, this numerical algorithm can discern whether some…
Particle physics experiments rely on the (generalised) likelihood ratio test (LRT) for searches and measurements, which consist of composite hypothesis tests. However, this test is not guaranteed to be optimal, as the Neyman-Pearson lemma…
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…
We consider testing for two-sample means of high dimensional populations by thresholding. Two tests are investigated, which are designed for better power performance when the two population mean vectors differ only in sparsely populated…
In solar physics, especially in exploratory stages of research, it is often necessary to compare the power spectra of two or more time series. One may, for instance, wish to estimate what the power spectrum of the combined data sets might…
Over the last decades, impressive progresses have been made in many experimental domains, e.g. microscopic techniques such as single-particle tracking, leading to plethoric amounts of data. In a large variety of systems, from natural to…
Power-law distributions are essential in computational and statistical investigations of extreme events and complex systems. The usual technique to generate power-law distributed data is to first infer the scale exponent $\alpha$ using the…