Related papers: On fitting power laws to ecological data
In this paper we introduce and study several multivariate, heavy-tailed distribution classes, and we explore their closure properties and their applications. We consider the class of multivariate, positively decreasing distributions, and…
Heavy-tailed probability distributions are extremely useful and play a crucial role in modeling different types of financial data sets. This study presents a two-pronged methodology. First, a mixture probability distribution is created by…
In some fields of applications of stable distributions, especially in economics, it appears, that data have distributions similar to stable in a large region, but do not have such heavy tails. Our aim in this note is to propose several…
The availability of large scale streaming network data has reinforced the ubiquity of power-law distributions in observations and enabled precision measurements of the distribution parameters. The increased accuracy of these measurements…
We investigate scaling properties of human brain functional networks in the resting-state. Analyzing network degree distributions, we statistically test whether their tails scale as power-law or not. Initial studies, based on least-squares…
It has been shown that some macroeconomic time series, especially those where outliers could be present, can be well modelled using heavy tailed distributions for the noise components. Methods for deciding when and where heavy-tailed models…
Real-world visual data often exhibits a long-tailed distribution, where some ''head'' classes have a large number of samples, yet only a few samples are available for ''tail'' classes. Such imbalanced distribution causes a great challenge…
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…
Recently, long-tailed image classification harvests lots of research attention, since the data distribution is long-tailed in many real-world situations. Piles of algorithms are devised to address the data imbalance problem by biasing the…
Identifying the statistical distribution that best fits citation data is important to allow robust and powerful quantitative analyses. Whilst previous studies have suggested that both the hooked power law and discretised lognormal…
We study how the presence of correlations in physical variables contributes to the form of probability distributions. We investigate a process with correlations in the variance generated by (i) a Gaussian or (ii) a truncated L\'{e}vy…
This review paper explores the evolution of discussions about "long-tail" scientific data in the scholarly literature. The "long-tail" concept, originally used to explain trends in digital consumer goods, was first applied to scientific…
Current-day genomes bear the mark of the evolutionary processes. One of the strongest indications is the sequence homology among families of proteins that perform similar biological functions in different species. The number of proteins in…
The Lindley distribution and its numerous generalizations are widely used in statistical and engineering practice. Recently, a power transformation of Lindley distribution, called the power Lindley distribution, has been introduced by M. E.…
Power law scaling is observed in many physical, biological and socio-economical complex systems and is now considered as an important property of these systems. In general, power law exists in the central part of the distribution. It has…
A novel statistical method is proposed and investigated for estimating a heavy tailed density under mild smoothness assumptions. Statistical analyses of heavy-tailed distributions are susceptible to the problem of sparse information in the…
Compound Poisson distributions have been employed by many authors to fit experimental data, typically via the method of moments or maximum likelihood estimation. We propose a new technique and apply it to several sets of published data. It…
In this paper we discuss the problem of the estimation of extreme event occurrence probability for data drawn from some multifractal process. We also study the heavy (power-law) tail behavior of probability density function associated with…
The Burr type XII (BXII) distribution has been largely used in different fields due to its great flexibility for fitting data. These applications have typically involved data showing heavy-tailed behaviors. In order to give more flexibility…
Many complex networks in natural and social phenomena have often been characterized by heavy-tailed degree distributions. However, due to rapidly growing size of network data and concerns on privacy issues about using these data, it becomes…