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Heavy-tailed distribution

About: Heavy-tailed distribution is a research topic. Over the lifetime, 2686 publications have been published within this topic receiving 87581 citations.


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Book
01 Jan 1994
TL;DR: Continuous Distributions (General) Normal Distributions Lognormal Distributions Inverse Gaussian (Wald) Distributions Cauchy Distribution Gamma Distributions Chi-Square Distributions Including Chi and Rayleigh Exponential Distributions Pareto Distributions Weibull Distributions Abbreviations Indexes
Abstract: Continuous Distributions (General) Normal Distributions Lognormal Distributions Inverse Gaussian (Wald) Distributions Cauchy Distribution Gamma Distributions Chi-Square Distributions Including Chi and Rayleigh Exponential Distributions Pareto Distributions Weibull Distributions Abbreviations Indexes

7,270 citations

Journal ArticleDOI
TL;DR: In this paper, a simple general approach to inference about the tail behavior of a distribution is proposed, which is not required to assume any global form for the distribution function, but merely the form of behavior in the tail where it is desired to draw inference.
Abstract: A simple general approach to inference about the tail behavior of a distribution is proposed. It is not required to assume any global form for the distribution function, but merely the form of behavior in the tail where it is desired to draw inference. Results are particularly simple for distributions of the Zipf type, i.e., where $G(y) = 1 - Cy^{-\alpha}$ for large $y$. The methods of inference are based upon an evaluation of the conditional likelihood for the parameters describing the tail behavior, given the values of the extreme order statistics, and can be implemented from both Bayesian and frequentist viewpoints.

3,060 citations

Journal ArticleDOI
C. Chow1, C. Liu1
TL;DR: It is shown that the procedure derived in this paper yields an approximation of a minimum difference in information when applied to empirical observations from an unknown distribution of tree dependence, and the procedure is the maximum-likelihood estimate of the distribution.
Abstract: A method is presented to approximate optimally an n -dimensional discrete probability distribution by a product of second-order distributions, or the distribution of the first-order tree dependence. The problem is to find an optimum set of n - 1 first order dependence relationship among the n variables. It is shown that the procedure derived in this paper yields an approximation of a minimum difference in information. It is further shown that when this procedure is applied to empirical observations from an unknown distribution of tree dependence, the procedure is the maximum-likelihood estimate of the distribution.

2,854 citations

Book
01 Nov 1989
TL;DR: In this article, the authors define marginal distributions, moments and density marginal distributions moments density the relationship between (phi and f) conditional distributions properties of elliptically symmetric distributions mixtures of normal distributions robust statistics and regression model robust statistics regression model log-elliptical and additive logistic elliptical distributions multivariate log elliptical distribution additive logistics elliptical distribution complex elliptical symmetric distribution.
Abstract: Part 1 Preliminaries: construction of symmetric multivariate distributions notation of algebraic entities and characteristics of random quantities the "d" operator groups and invariance dirichlet distribution problems 1. Part 2 Spherically and elliptically symmetric distributions: introduction and definition marginal distributions, moments and density marginal distributions moments density the relationship between (phi) and f conditional distributions properties of elliptically symmetric distributions mixtures of normal distributions robust statistics and regression model robust statistics regression model log-elliptical and additive logistic elliptical distributions multivariate log-elliptical distribution additive logistic elliptical distributions complex elliptically symmetric distributions. Part 3 Some subclasses of elliptical distributions: multiuniform distribution the characteristic function moments marginal distribution conditional distributions uniform distribution in the unit sphere discussion symmetric Kotz type distributions definition distribution of R(2) moments multivariate normal distributions the c.f. of Kotz type distributions symmetric multivariate Pearson type VII distributions definition marginal densities conditional distributions moments conditional distributions moments some examples extended Tn family relationships between Ln and Tn families of distributions order statistics mixtures of exponential distributions independence, robustness and characterizations problems V. Part 6 Multivariate Liouville distributions: definitions and properties examples marginal distributions conditional distribution characterizations scale-invariant statistics survival functions inequalities and applications.

2,106 citations

Book
01 Jan 1986
TL;DR: In this article, the authors present examples of stable laws in applications, including analytical properties of the distributions in the family, special properties of laws in the class, and estimators of the parameters of stable distributions.
Abstract: Examples of stable laws in applications Analytic properties of the distributions in the family $\mathfrak S$ Special properties of laws in the class $\mathfrak W$ Estimators of the parameters of stable distributions.

1,707 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20241
202318
202234
202165
202044
201948