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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…

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…

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…

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…

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…

The so-called Pareto-Levy or power-law distribution has been successfully used as a model to describe probabilities associated to extreme variations of worldwide stock markets indexes data and it has the form $Pr(X>x) ~ x**(-alpha) for…

Power law distributions are widely observed in chemical physics, geophysics, biology, and beyond. The independent variable x of these distributions has an obligatory lower bound and in many cases also an upper bound. Estimating these bounds…

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…

We derive a parallel sampling algorithm for computational inverse problems that present an unknown linear forcing term and a vector of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of…

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…

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…

Power law or generalized polynomial regressions with unknown real-valued exponents and coefficients, and weakly dependent errors, are considered for observations over time, space or space--time. Consistency and asymptotic normality of…

In this paper we consider the problem of estimating a parameter of a probability distribution when we have some prior information on a nuisance parameter. We start by the very simple case where we know perfectly the value of the nuisance…

This paper describes a simple procedure to estimate the parameters of the univariate truncated normal and lognormal distributions by maximum likelihood. It starts from a reparameterization of the lognormal that was previously introduced by…

In this paper, a new three-parameter lifetime distribution is introduced and many of its standard properties are discussed. These include shape of the probability density function, hazard rate function and its shape, quantile function,…

The unknown amplitude law q(x) defining an observed effect may be found using the principle of Extreme Physical Information. EPI is derived as follows. The observations follow an information flow J --> I, with J the information intrinsic to…

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…

We investigate the problem of best policy identification in discounted linear Markov Decision Processes in the fixed confidence setting under a generative model. We first derive an instance-specific lower bound on the expected number of…

I present an analytic method for estimating the errors in fitting a distribution. A well-known theorem from statistics gives the minimum variance bound (MVB) for the uncertainty in estimating a set of parameters $\l_i$, when a distribution…

Over the last decades, impressive progresses have been made in many experimental domains, e.g. microscopic techniques such as single-particle tracking, leading to plethoric amounts of data. In a large variety of systems, from natural to…