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In Hempel's paradox of the ravens, seeing a red pencil is considered as supporting evidence that all ravens are black. Also known as the Paradox of Confirmation, the paradox and its many resolutions indicate that we cannot underestimate the…
A length dependence of the effective mobility in the form of a power law, B ~ L^(1-1/alpha) is observed in dispersive transport in amorphous substances, with 0 < \alpha < 1. We deduce this behavior as a simple consequence of the statistical…
In this note, we use a toy problem of detecting cycles of length two in a tent map to highlight some curious phenomena in the behavior of discrete dynamical systems. This work presents no new results or proofs, only computer experiments and…
Despite its importance to experimental design, statistical power (the probability that, given a real effect, an experiment will reject the null hypothesis) has largely been ignored by the NLP community. Underpowered experiments make it more…
Fractal properties are usually characterized by means of various statistical tools which deal with spatial average quantities. Here we focus on the determination of fluctuations around the average counts and we develop a test for the study…
Investigations of isotope shifts of atomic spectral lines provide insights into nuclear properties. Deviations from the linear dependence of the isotope shifts of two atomic transitions on nuclear parameters, leading to a nonlinearity of…
In the presence of a layer of metaprobabilities (from uncertainty concerning the parameters), the asymptotic tail exponent corresponds to the lowest possible tail exponent regardless of its probability. The problem explains "Black Swan"…
Skewness and kurtosis are fundamental statistical moments commonly used to quantify asymmetry and tail behavior in probability distributions. Despite their widespread application in statistical mechanics, condensed matter physics, and…
We study the statistics of human deaths from wars, conflicts, similar man-made conflicts as well as natural disasters. The probability distribution of number of people killed in natural disasters as well as man made situations show power…
Classical collisions with an ideal gas generate non-Maxwellian distribution functions for a single ion in a radio frequency ion trap. The distributions have power-law tails whose exponent depends on the ratio of buffer gas to ion mass. This…
Benford's law is often used as a support to critical decisions related to data quality or the presence of data manipulations or even fraud. However, many authors argue that conventional statistical tests will reject the null of data…
In this paper, we address the question of comparison between populations of trees. We study an statistical test based on the distance between empirical mean trees, as an analog of the two sample z statistic for comparing two means. Despite…
The conventional perspective on Markov chains considers decision problems concerning the probabilities of temporal properties being satisfied by traces of visited states. However, consider the following query made of a stochastic system…
Drawdowns are essential aspects of risk assessment in investment management. They offer a more natural measure of real market risks than the variance or other cumulants of daily (or some other fixed time scale) distributions of returns.…
Dynamical systems in nature exhibit selfsimilar fractal fluctuations and the corresponding power spectra follow inverse power law form signifying long-range space-time correlations identified as self-organized criticality. The physics of…
Stochastic models, based on random processes, may lead to power law distributions, which provide long range correlations. The observation of power law behavior and the presence of long range correlations in biological systems has been…
We propose the test for distinguishing between two classes of distribution tails using only the largest order statistics of the sample and state its consistency. We do not assume belonging the corresponding distribution functions to any…
Dwarf galaxies are ideal laboratories to test dark matter models and alternative theories because their dynamical mass (from observed kinematics) largely outweighs their baryonic mass (from gas and stars). In most star-forming dwarfs, cold…
We discuss the prospects of measuring deviations of the dark energy equation of state from w=-1 by using the swampland conjectures to relate inflationary models to quintessence scenarios. This note is based on work done by the author with…
Renewal processes with heavy-tailed power law distributed sojourn times are commonly encountered in physical modelling and so typical fluctuations of observables of interest have been investigated in detail. To describe rare events the rate…