Bibliography on stable distributions, processes and related topics
01 Jan 2004-
TL;DR: The following sections are a start on organizing references on stable distributions by topic, and please provide all references in BibTeX form, especially if you have more than one or two additions.
Abstract: The following sections are a start on organizing references on stable distributions by topic. It is far from complete. Starting on page 18 there is an extensive list of papers on stable distributions, many of which are not included in the first section. Some of the papers there do not directly refer to stable distributions. Someday I may have the time to edit those out, but for now please ignore those references. This list includes a bibliography file provided by Gena Samorodnitsky from Cornell University. I would like to keep this list correct and up-to-date. If you have corrections or additions, please e-mail them to me at the above address, and suggest where to place your references in one of the sections below. A sentence or two summarizing the content would be useful. Please provide all references in BibTeX form, especially if you have more than one or two additions. (See http://en.wikipedia.org/wiki/BibTeX for basic information on BibTEX.) Please send a copy of your papers along.
Citations
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TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
Abstract: Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.
5,689 citations
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TL;DR: In this article, a computer program for modelling financial time series is presented, based on the Random Walk Hypothesis, which is used to forecast trends in prices in futures markets.
Abstract: Features of Financial Returns Modelling Price Volatility Forecasting Standard Deviations The Accuracy of Autocorrelation Estimates Testing the Random Walk Hypothesis Forecasting Trends in Prices Evidence Against the Efficiency of Futures Markets Valuing Options Appendix: A Computer Program for Modelling Financial Time Series.
1,115 citations
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TL;DR: In this article, the authors generalise l'estimateur bien connu de Hill de lindice d a fonction de reparatition avec queue de variation reguliere a une estimation de l'indice of a loi de valeurs extremes.
Abstract: On generalise l'estimateur bien connu de Hill de l'indice d'une fonction de reparatition avec queue de variation reguliere a une estimation de l'indice d'une loi de valeurs extremes. On demontre la convergence et la normalite asymptotique. On utilise l'estimateur pour certaines estimations comme celle d'une quantile elevee et d'un point d'extremite
655 citations
References
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01 Jan 1993TL;DR: This article presents bootstrap methods for estimation, using simple arguments, with Minitab macros for implementing these methods, as well as some examples of how these methods could be used for estimation purposes.
Abstract: This article presents bootstrap methods for estimation, using simple arguments. Minitab macros for implementing these methods are given.
37,183 citations
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TL;DR: A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
Abstract: Systems as diverse as genetic networks or the World Wide Web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature was found to be a consequence of two generic mechanisms: (i) networks expand continuously by the addition of new vertices, and (ii) new vertices attach preferentially to sites that are already well connected. A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
33,771 citations
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01 Jan 195031,532 citations
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01 Jan 1943
TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
Abstract: 0 Introduction 1 Elementary Functions 2 Indefinite Integrals of Elementary Functions 3 Definite Integrals of Elementary Functions 4.Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integrals of Special Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequalities 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
27,354 citations
"Bibliography on stable distribution..." refers background in this paper
...Graff (1995). Real estate is not normal: a fresh look at real estate return distributions....
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TL;DR: A method is described for the minimization of a function of n variables, which depends on the comparison of function values at the (n 41) vertices of a general simplex, followed by the replacement of the vertex with the highest value by another point.
Abstract: A method is described for the minimization of a function of n variables, which depends on the comparison of function values at the (n 41) vertices of a general simplex, followed by the replacement of the vertex with the highest value by another point. The simplex adapts itself to the local landscape, and contracts on to the final minimum. The method is shown to be effective and computationally compact. A procedure is given for the estimation of the Hessian matrix in the neighbourhood of the minimum, needed in statistical estimation problems.
27,271 citations