Related papers: Fitting Power-laws in empirical data with estimato…
The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the…
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…
Maximum likelihood estimation and a test of fit based on the Anderson-Darling statistic is presented for the case of the power law distribution when the parameters are estimated from a left-censored sample. Expressions for the maximum…
A simple fragmentation model is introduced and analysed. We show that, under very general conditions, an effective power law for the mass distribution arises with realistic exponent. This exponent has a universal limit, but in practice the…
Maximum pseudolikelihood (MPL) estimators are useful alternatives to maximum likelihood (ML) estimators when likelihood functions are more difficult to manipulate than their marginal and conditional components. Furthermore, MPL estimators…
In the last years, researchers have realized the difficulties of fitting power-law distributions properly. These difficulties are higher in Zipf's systems, due to the discreteness of the variables and to the existence of two representations…
In this work we consider data-driven optimization problems where one must maximize a function given only queries at a fixed set of points. This problem setting emerges in many domains where function evaluation is a complex and expensive…
Advanced science and technology provide a wealth of big data from different sources for extreme value analysis. Classical extreme value theory was extended to obtain an accelerated max-stable distribution family for modelling competing…
We provide an efficient unified plug-in approach for estimating symmetric properties of distributions given $n$ independent samples. Our estimator is based on profile-maximum-likelihood (PML) and is sample optimal for estimating various…
In nature or societies, the power-law is present ubiquitously, and then it is important to investigate the mathematical characteristics of power-laws in the recent era of big data. In this paper we prove the superposition of non-identical…
Modeling distributions of citations to scientific papers is crucial for understanding how science develops. However, there is a considerable empirical controversy on which statistical model fits the citation distributions best. This paper…
This paper presents some results on the maximum likelihood (ML) estimation from incomplete data. Finite sample properties of conditional observed information matrices are established. They possess positive definiteness and the same Loewner…
If the log likelihood is approximately quadratic with constant Hessian, then the maximum likelihood estimator (MLE) is approximately normally distributed. No other assumptions are required. We do not need independent and identically…
In this article, we construct semiparametrically efficient estimators of linear functionals of a probability measure in the presence of side information using an easy empirical likelihood approach. We use estimated constraint functions and…
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…
To know the statistical distribution of a variable is an important problem in management of resources. Distributions of the power law type are observed in many real systems. However power law distributions have an infinite variance and thus…
The prevailing maximum likelihood estimators for inferring power law models from rank-frequency data are biased. The source of this bias is an inappropriate likelihood function. The correct likelihood function is derived and shown to be…
In this paper, we propose an optimization-based mechanism to explain power law distributions, where the function that the optimization process is seeking to optimize is derived mathematically, then the behavior and interpretation of this…
Scale-free networks play a fundamental role in the study of complex networks and various applied fields due to their ability to model a wide range of real-world systems. A key characteristic of these networks is their degree distribution,…
Many man-made and natural phenomena, including the intensity of earthquakes, population of cities and size of international wars, are believed to follow power-law distributions. The accurate identification of power-law patterns has…