Related papers: Testing Universality in Critical Exponents: the Ca…
More than one billion data sampled with different frequencies from several financial instruments were investigated with the aim of testing whether they involve power law. As a result, a known power law with the power exponent around -4 was…
Zipf's power-law distribution is a generic empirical statistical regularity found in many complex systems. However, rather than universality with a single power-law exponent (equal to 1 for Zipf's law), there are many reported deviations…
The size or energy of diverse structures or phenomena in geoscience appears to follow power-law distributions. A rigorous statistical analysis of such observations is tricky, though. Observables can span several orders of magnitude, but the…
Power-law type probability density functions spanning several orders of magnitude are found for different avalanche properties. We propose a methodology to overcome empirical constrains that limit the power-law range for the distributions…
A long noted difficulty when assessing the reliability (or calibration) of forecasting systems is that reliability, in general, is a hypothesis not about a finite dimensional parameter but about an entire functional relationship. A…
Meteorological parameters, such as temperature, rainfall, pressure etc., exhibit selfsimilar space-time fractal fluctuations generic to dynamical systems in nature such as fluid flows, spread of forest fires, earthquakes, etc. The power…
Power-law type distributions are extensively found when studying the behaviour of many complex systems. However, due to limitations in data acquisition, empirical datasets often only cover a narrow range of observation, making it difficult…
When the outcome of interest is semicontinuous and collected longitudinally, efficient testing can be difficult. Daily rainfall data is an excellent example which we use to illustrate the various challenges. Even under the simplest…
Many natural processes exhibit power-law behavior. The power-law exponent is linked to the underlying physical process and therefore its precise value is of interest. With respect to the energy content of nanoflares, for example, a…
We review briefly the concepts underlying complex systems and probability distributions. The later are often taken as the first quantitative characteristics of complex systems, allowing one to detect the possible occurrence of regularities…
We analyze distributions of rain-event sizes, rain-event durations, and dry-spell durations for data obtained from a network of 20 rain gauges scattered in a region of the NW Mediterranean coast. While power-law distributions model the…
In this work, we revisit the problem of uniformity testing of discrete probability distributions. A fundamental problem in distribution testing, testing uniformity over a known domain has been addressed over a significant line of works, and…
Power-law distributions occur in wide variety of physical, biological, and social phenomena. In this paper, we propose a statistical hypothesis test based on the log-likelihood ratio to assess whether two samples of discrete data are drawn…
In this paper, we revisit the classical goodness-of-fit problems for univariate distributions; we propose a new testing procedure based on a characterisation of the uniform distribution. Asymptotic theory for the simple hypothesis case is…
The statistics of natural catastrophes contains very counter-intuitive results. Using earthquakes as a working example, we show that the energy radiated by such events follows a power-law or Pareto distribution. This means, in theory, that…
We reconsider a well known problem of quantum theory, i.e. the so called measurement (or macro-objectification) problem, and we rederive the fact that it gives rise to serious problems of interpretation. The novelty of our approach derives…
Jamming and percolation transitions in the standard random sequential adsorption of particles on regular lattices are characterized by a universal set of critical exponents. The universality class is preserved even in the presence of…
Numerous weather parameters affect the occurrence and amount of rainfall. Therefore, it is important to study these parameters and their interdependency. In this paper, different weather and time-related variables -- relative humidity,…
We discuss several models in order to shed light on the origin of power-law distributions and power-law correlations in financial time series. From an empirical point of view, the exponents describing the tails of the price increments…
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…