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We introduce two ratio-based robust test statistics, max-robust-sum (MRS) and sum-robust-sum (SRS), designed to enhance the robustness of outlier detection in samples with exponential or Pareto tails. We also reintroduce the inward…
We consider current observational constraints on the electromagnetic charge of dark matter. The velocity dependence of the scattering cross-section through the photon gives rise to qualitatively different constraints than standard dark…
The shape of the luminosity function of white dwarfs (WDLF) is sensitive to the characteristic cooling time and, therefore, it can be used to test the existence of additional sources or sinks of energy such as those predicted by alternative…
The importance of the power law has been well realized in econophysics over the last decade. For instance, the distribution of the rate of stock price variation and of personal assets show the power law. While these results reveal the…
Taylor's power law (or fluctuation scaling) states that on comparable populations, the variance of each sample is approximately proportional to a power of the mean of the population. It has been shown to hold by empirical observations in a…
The power law is useful in describing count phenomena such as network degrees and word frequencies. With a single parameter, it captures the main feature that the frequencies are linear on the log-log scale. Nevertheless, there have been…
Most parametrizations for dark energy involve the equation of state $w$ of the dark energy. In this work, we choose the pressure of the dark energy to parametrize. As $p = constant$ essentially gives a cosmological constant, we use the…
Large deviation theory quantifies the occurence of events that deviate from the average behavior of a system. Such events arise from non-typical trajectories of the dynamics. In this note we derive the time evolution of these rare…
We discuss the possibility of exploring an unbroken U(1) gauge interaction in the dark sector by means of gravitational waves. Dark sector states charged under the dark force can give a macroscopic charge to astronomical bodies. Yet the…
Modeling distributions of citations to scientific papers is crucial for understanding how science develops. However, there is a considerable empirical controversy on which statistical model fits the citation distributions best. This paper…
Natural language data follows a power-law distribution, with most knowledge and skills appearing at very low frequency. While a common intuition suggests that reweighting or curating data towards a uniform distribution may help models…
This paper introduces nonparametric econometric methods that characterize general power law distributions under basic stability conditions. These methods extend the literature on power laws in the social sciences in several directions.…
In the last years, researchers have realized the difficulties of fitting power-law distributions properly. These difficulties are higher in Zipf's systems, due to the discreteness of the variables and to the existence of two representations…
In this paper we consider suitable families of power series distributed random variables, and we study their asymptotic behavior in the fashion of large (and moderate) deviations. We also present two examples of fractional counting…
We consider a population with non-overlapping generations, whose size goes to infinity. It is described by a discrete genealogy which may be time non-homogeneous and we pay special attention to branching trees in varying environments. A…
Turbulence is generally associated with universal power-law spectra in scale ranges without significant drive or damping. Although many examples of turbulent systems do not exhibit such an inertial range, power-law spectra may still be…
Spectra in astroparticle physics are commonly approximated by simple power laws. The steeply falling nature of these power laws, however, makes the detection of additional components rather challenging. This holds true especially, if the…
In combination with post-selection, weak measurements can lead to surprising results known as anomalous weak values. These lie outside the bounds of the spectrum of the relevant observable, as in the canonical example of measuring the spin…
The physical nature of the currently observed dark energy in the universe is completely unclear, and many different theoretical models co-exist. Nevertheless, if dark energy is produced by vacuum fluctuations then there is a chance to probe…
This paper studies a random differential equation with random switch perturbations. We explore how the maximum displacement from the equilibrium state depends on the statistical properties of time series of {the} random switches. We show a…