Related papers: Analysis of power-law exponents by maximum-likelih…
Distributions following a power-law are an ubiquitous phenomenon. Methods for determining the exponent of a power-law tail by graphical means are often used in practice but are intrinsically unreliable. Maximum likelihood estimators for the…
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…
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…
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…
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,…
We study maximum likelihood estimation in log-linear models under conditional Poisson sampling schemes. We derive necessary and sufficient conditions for existence of the maximum likelihood estimator (MLE) of the model parameters and…
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…
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…
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…
The normality assumption on data set is very restrictive approach for modelling. The generalized form of normal distribution, named as an exponential power (EP) distribution, and its scale mixture form have been considered extensively to…
The maximum likelihood principle is widely used in statistics, and the associated estimators often display good properties. indeed maximum likelihood estimators are guaranteed to be asymptotically efficient under mild conditions. However in…
Designing reliable networks consists in finding topological structures, which are able to successfully carry out desired processes and operations. When this set of activities performed within a network are unknown and the only available…
Probability distributions and densities are derived for the excess and deficiency of the intensity or instantaneous energy (quasi-static power) associated with a $p$-dimensional random vector field. Explicit expressions for the exact…
Many experimental quantities show a power-law distribution $p(x)\propto x^{-\alpha}$. In astrophysics, examples are: size distribution of dust grains or luminosity function of galaxies. Such distributions are characterized by the exponent…
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…
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…
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…
Multiple root estimation problems in statistical inference arise in many contexts in the literature. In the context of maximum likelihood estimation, the existence of multiple roots causes uncertainty in the computation of maximum…
Loss tomography has been studied for more than 10 years and a number of estimators have been proposed. The estimators can be divided into two classes: maximum likelihood and non-maximum likelihood. The maximum likelihood estimators rely on…
Multivariate extreme-value analysis is concerned with the extremes in a multivariate random sample, that is, points of which at least some components have exceptionally large values. Mathematical theory suggests the use of max-stable models…