Related papers: Parameter estimation for power-law distributions b…
Maximum likelihood estimation in statistics leads to the problem of maximizing a product of powers of polynomials. We study the algebraic degree of the critical equations of this optimization problem. This degree is related to the number of…
The extreme value index is a fundamental parameter in univariate Extreme Value Theory (EVT). It captures the tail behavior of a distribution and is central in the extrapolation beyond observed data. Among other semi-parametric methods (such…
Due to its heavy-tailed and fully parametric form, the multivariate generalized Gaussian distribution (MGGD) has been receiving much attention for modeling extreme events in signal and image processing applications. Considering the…
In finite mixtures of location-scale distributions, if there is no constraint or penalty on the parameters, then the maximum likelihood estimator does not exist because the likelihood is unbounded. To avoid this problem, we consider a…
We consider the problem of estimating the distribution underlying an observed sample of data. Instead of maximum likelihood, which maximizes the probability of the ob served values, we propose a different estimate, the high-profile…
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…
Determining the power distribution of the members of a shareholder meeting or a legislative committee is a well-known problem for many applications. In some cases it turns out that power is nearly proportional to relative voting weights,…
We show how recent results by Bening and Korolev in the context of estimation, when linked with a classical result of Fisher concerning the negative binomial distribution, can be used to explain the ubiquity of power law probability…
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…
In this paper the maximum likelihood equations for the parameters of the Weight Lindley distribution are studied considering different types of censoring, such as, type I, type II and random censoring mechanism. A numerical simulation study…
The power-law distribution is ubiquitous and its mechanism seems to be various. We find a general mechanism for the distribution. The distribution of a geometrically growing system can be approximated by a log - completely squared chi…
In the current paper, the estimation of the probability density function and the cumulative distribution function of the Topp-Leone distribution is considered. We derive the following estimators: maximum likelihood estimator, uniformly…
The controlled branching process is a generalization of the classical Bienaym\'e-Galton-Watson branching process. It is a useful model for describing the evolution of populations in which the population size at each generation needs to be…
Loynes' distribution, which characterizes the one dimensional marginal of the stationary solution to Lindley's recursion, possesses an ultimately exponential tail for a large class of increment processes. If one can observe increments but…
We consider a model for chaotic diffusion with amplification on graphs associated with piecewise-linear maps of the interval. We investigate the possibility of having power-law tails in the invariant measure by approximate solution of the…
We derive an extended empirical likelihood for parameters defined by estimating equations which generalizes the original empirical likelihood for such parameters to the full parameter space. Under mild conditions, the extended empirical…
We suggest approximating the distribution of the sum of independent and identically distributed random variables with a Pareto-like tail by combining extreme value approximations for the largest summands with a normal approximation for the…
Learning the parameters of graphical models using the maximum likelihood estimation is generally hard which requires an approximation. Maximum composite likelihood estimations are statistical approximations of the maximum likelihood…
In exploratory factor analysis, model parameters are usually estimated by maximum likelihood method. The maximum likelihood estimate is obtained by solving a complicated multivariate algebraic equation. Since the solution to the equation is…
It is demonstrated that World War II casualty data display statistical structure that would be expected from multifractal data. Given that the data displayed these properties, it is shown how the existence of power-law tails in the…