相关论文: Parameter estimation for power-law distributions b…
Maximum-likelihood exponent maps have been studied as a technique to increase the understanding and improve the fit of power-law exponents to experimental and numerical simulation data, especially when they exhibit both upper and lower…
Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is…
A wide range of natural and social phenomena result in observables whose distributions can be well approximated by a power-law decay. The well-known Hill estimator of the tail exponent provides results which are in many respects superior to…
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…
In this paper we tackle the problem of estimating the power-law tail exponent of income distributions by using the Hill's estimator. A subsample semi-parametric bootstrap procedure minimising the mean squared error is used to choose the…
Distinguishing power-law distributions from other heavy-tailed distributions is challenging, and this task is often further complicated by subsampling effects. In this work, we evaluate the performance of two commonly used methods for…
We characterize the existence of the maximum likelihood estimator for discrete exponential families. Our criterion is simple to apply as we show in various settings, most notably for exponential models of random graphs. As an application,…
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…
Max-stable distributions and processes are important models for extreme events and the assessment of tail risks. The full, multivariate likelihood of a parametric max-stable distribution is complicated and only recent advances enable its…
It has been repeatedly stated that maximum likelihood (ML) estimates of exponents of power-law distributions can only be reliably obtained for exponents smaller than minus one. The main argument that power laws are otherwise not…
Heavy-tailed or power-law distributions are becoming increasingly common in biological literature. A wide range of biological data has been fitted to distributions with heavy tails. Many of these studies use simple fitting methods to find…
This paper considers the problem of estimating a power-law degree distribution of an undirected network using sampled data. Although power-law degree distributions are ubiquitous in nature, the widely used parametric methods for estimating…
Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…
Maximum likelihood estimation is a common method of estimating the parameters of the probability distribution from a given sample. This paper aims to introduce the maximum likelihood estimation in the framework of sublinear expectation. We…
Linear systems with many degrees of freedom containing multiplicative and additive noise are considered. The steady state probability distribution for equations of this kind is examined. With multiplicative white noise it is shown that…
Consider a random sample from a bivariate distribution function $F$ in the max-domain of attraction of an extreme-value distribution function $G$. This $G$ is characterized by two extreme-value indices and a spectral measure, the latter…
Power laws pervade statistical physics and complex systems, but, traditionally, researchers in these fields have paid little attention to properly fit these distributions. Who has not seen (or even shown) a log-log plot of a completely…
Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law…
The three-parameter generalized extreme value distribution arises from classical univariate extreme value theory and is in common use for analyzing the far tail of observed phenomena. Curiously, important asymptotic properties of…
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…