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J. Tiago de Oliveira

Other affiliations: IAC, Sciences Academy of Lisbon
Bio: J. Tiago de Oliveira is an academic researcher from University of Lisbon. The author has contributed to research in topics: Gumbel distribution & Univariate. The author has an hindex of 11, co-authored 28 publications receiving 2338 citations. Previous affiliations of J. Tiago de Oliveira include IAC & Sciences Academy of Lisbon.

Papers
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Journal ArticleDOI
TL;DR: In this paper, the authors analyze the recent development of the theory of the asymptotic distribution of extremes in the light of the questions (i) and (ii). Several dependence concepts will be introduced, each of which leads to a solution of (i).
Abstract: Abstract. Let X j denote the life length of the j th component of a machine. In reliability theory, one is interested in the life length Z n of the machine where n signifies its number of components. Evidently, Z n = min (X j : 1 ≤ j ≤ n). Another important problem, which is extensively discussed in the literature, is the service time W n of a machine with n components. If Y j is the time period required for servicing the j th component, then W n = max (Y j : 1 ≤ j ≤ n). In the early investigations, it was usually assumed that the X's or Y's are stochastically independent and identically distributed random variables. If n is large, then asymptotic theory is used for describing Z n or W n . Classical theory thus gives that the (asymptotic) distribution of these extremes (Z n or W n ) is of Weibull type. While the independence assumptions are practically never satisfied, data usually fits well the assumed Weibull distribution. This contradictory situation leads to the following mathematical problems: (i) What type of dependence property of the X's (or the Y's) will result in a Weibull distribution as the asymptotic law of Z n (or W n )? (ii) given the dependence structure of the X's (or Y's), what type of new asymptotic laws can be obtained for Z n (or W n )? The aim of the present paper is to analyze the recent development of the (mathematical) theory of the asymptotic distribution of extremes in the light of the questions (i) and (ii). Several dependence concepts will be introduced, each of which leads to a solution of (i). In regard to (ii), the following result holds: the class of limit laws of extremes for exchangeable variables is identical to the class of limit laws of extremes for arbitrary random variables. One can therefore limit attention to exchangeable variables. The basic references to this paper are the author's recent papers in Duke Math. J. 40 (1973), 581–586, J. Appl. Probability 10 (1973, 122–129 and 11 (1974), 219–222 and Zeitschrift fur Wahrscheinlichkeitstheorie 32 (1975), 197–207. For multivariate extensions see H. A. David and the author, J. Appl. Probability 11 (1974), 762–770 and the author's paper in J. Amer. Statist. Assoc. 70 (1975), 674–680. Finally, we shall point out the difficulty of distinguishing between several distributions based on data. Hence, only a combination of theoretical results and experimentations can be used as conclusive evidence on the laws governing the behavior of extremes.

1,964 citations

BookDOI
01 Jan 1984
TL;DR: In this paper, the authors present an overview of the application of extreme values in meteorology, structural engineering, and insurance mathematics, using the Gumbel model and the Box-Jenkins model.
Abstract: A - Core Course.- Inaugural Address: Statistical Extremes: Theory and Applications, Motivation and Perspectives.- Introduction, Order Statistics, Exceedances. Laws of Large Numbers.- Asymptotics Stable Laws for Extremes. Tail Properties.- Slow Variation and Characterization of Domains of Attraction.- Introduction, Gumbel Model.- Statistical Estimation of Parameters of the Weibull and Frechet Distributions.- Univariate Extremes Statistical Choice.- Statistical Estimation in Extreme Value Theory.- Probabilistic Aspects of Multivariate Extremes.- Bivariate Models for Extremes Statistical Decision.- Extremes in Dependent Random Sequences.- Extremes in Continuous Stochastic Processes.- Comparison Technique for Highly Dependent Stationary Gaussian Processes.- Extremes in Hydrology.- Application of Extreme Values in Structural Engineering.- Extremes in Meteorology.- Extreme Values in Insurance Mathematics.- B - Specific Lectures.- Use and Structure of Slepian Model. Processes for Prediction and Detection in Crossing and Extreme Value Theory.- Spline and Isotonic Estimation of the Pareto Function.- Extremal Processes.- Extreme Values for Sequences of Stable Random Variables.- C - Workshops.- Large Deviations of Extremes.- Uniform Rates of Convergence to Extreme Value Distributions.- Rates of Convergence in Extreme Value Theory.- Concomitants in a Multidimensional Extreme Model.- A Short Cut Algorithm for Obtaining Coefficients of the BLUE's.- Statistical Choice of Univariate Extreme Models. Part II.- Doubly Exponential Random Number Generators.- Probability Problems in Seismic Risk and Load Combinations for Power Plants.- D - Contributed Papers.- The Distribution of the Maximal Time till Departure from a State in a Markov Chain.- The Box-Jenkins Model and the Progressive Fatigue Failure of Large Parallel Element Stay Tendons.- The Asymptotic Behaviour of the Maximum Likelihood Estimates for Univariate Extremes.- On Upper and Lower Extremes in Stationary Sequences.- Modelling Excesses over High Thresholds, with an Application.- Stationary Min-stable Stochastic Processes.- Strong Approximations of Records and Record Times.- High Percentiles Atmospheric SO2-Concentrations in Belgium.- Extreme Response of the Linear Oscillator with Modulated Random Excitation.- Frost Data: A Case Study on Extreme Values of Non-Stationary Sequences.- Estimation of the Scale and Location Parameters of the Extreme Value (Gumbel) Distribution for Large Censored Samples.- Asymptotic Behaviour of the Extreme Order Statistics in the Non-Identically Distributed Case.- Limit Distribution of the Minimum Distance between Independent and Identically Distributed d-Dimensional Random Variables.- Approximate Values for the Moments of Extreme Order Statistics in Large Samples.- Estimation of Parameters of Extreme Order Distributions of Exponential Type Parents.- On Ordered Uniform Spacings for Testing Goodness of Fit.- Inequalities for the Relative Sufficiency between Sets of Order Statistics.- POT-Estimation of Extreme Sea States and the Benefit of Using Wind Data.- Threshold Methods for Sample Extremes.- On Successive Record Values in a Sequence of Independent Identically Distributed Random Variables.- Two Test Statistics for Choice of Univariate Extreme Models.- On the Asymptotic Uperossings of a Class of Non-Stationary Sequences.- Author Index.

141 citations

Journal ArticleDOI
TL;DR: The Shewhart control chart for means can be made more sensitive to small changes by adding a pair of warning limits, located inside the action limits, and taking action when a run of a specified number of consecutive means falls between the warning and action limits.
Abstract: The Shewhart control chart for means can be made more sensitive to small changes by adding a pair of warning limits, located inside the action limits, and taking action when a run of a specified number of consecutive means falls between the warning and ..

35 citations

Book ChapterDOI
01 Jan 1984
TL;DR: In this article, the authors describe the asymptotic distribution of bivariate samples of maxima, with Gumbel margins, some important correlation and regression results are given, and statistical decision related to them is presented.
Abstract: After describing the asymptotic distribution of bivariate samples of maxima, with Gumbel margins, some important correlation and regression results are given. The five models known until now (logistic, mixed, Gumbel, biextremal and natural) are described and statistical decision related to them is presented. Finally, a triextremal model is described.

27 citations

Book ChapterDOI
TL;DR: In this paper, a dependence function for extreme random pairs with Gumbel margins was obtained for the distribution function in the case of maxima, or for the survival function in case of minima.
Abstract: Bivariate extreme random pairs, with extreme margins, have for the distribution function, in the case of maxima, or for the survival function, in the case of minima, a dependence function. For the cases of Gumbel margins for maxima or of the exponential margins for minima an index of dependence as well the correlation coefficient are obtained; analogous results could be obtained for other margins and also study the non-parametric correlation coefficients.

23 citations


Cited by
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Book
01 Jan 2006
TL;DR: In this paper, the authors provide a comprehensive treatment of the problem of predicting individual sequences using expert advice, a general framework within which many related problems can be cast and discussed, such as repeated game playing, adaptive data compression, sequential investment in the stock market, sequential pattern analysis, and several other problems.
Abstract: This important text and reference for researchers and students in machine learning, game theory, statistics and information theory offers a comprehensive treatment of the problem of predicting individual sequences. Unlike standard statistical approaches to forecasting, prediction of individual sequences does not impose any probabilistic assumption on the data-generating mechanism. Yet, prediction algorithms can be constructed that work well for all possible sequences, in the sense that their performance is always nearly as good as the best forecasting strategy in a given reference class. The central theme is the model of prediction using expert advice, a general framework within which many related problems can be cast and discussed. Repeated game playing, adaptive data compression, sequential investment in the stock market, sequential pattern analysis, and several other problems are viewed as instances of the experts' framework and analyzed from a common nonstochastic standpoint that often reveals new and intriguing connections.

3,615 citations

Journal ArticleDOI
TL;DR: In this article, Modelling Extremal Events for Insurance and Finance is discussed. But the authors focus on the modeling of extreme events for insurance and finance, and do not consider the effects of cyber-attacks.
Abstract: (2002). Modelling Extremal Events for Insurance and Finance. Journal of the American Statistical Association: Vol. 97, No. 457, pp. 360-360.

2,729 citations

Book ChapterDOI
01 Jan 2002
TL;DR: This article deals with the static (nontime- dependent) case and emphasizes the copula representation of dependence for a random vector and the problem of finding multivariate models which are consistent with prespecified marginal distributions and correlations is addressed.
Abstract: Modern risk management calls for an understanding of stochastic dependence going beyond simple linear correlation. This paper deals with the static (non-time-dependent) case and emphasizes the copula representation of dependence for a random vector. Linear correlation is a natural dependence measure for multivariate normally and, more generally, elliptically distributed risks but other dependence concepts like comonotonicity and rank correlation should also be understood by the risk management practitioner. Using counterexamples the falsity of some commonly held views on correlation is demonstrated; in general, these fallacies arise from the naive assumption that dependence properties of the elliptical world also hold in the non-elliptical world. In particular, the problem of finding multivariate models which are consistent with prespecified marginal distributions and correlations is addressed. Pitfalls are highlighted and simulation algorithms avoiding these problems are constructed.

2,052 citations

Journal ArticleDOI
TL;DR: In this article, the authors consider the estimation of a stochastic frontier production function, which is the type introduced by Aigner, Lovell, and Schmidt (1977) and Meeusen and van den Broeck (1977).
Abstract: This article considers estimation of a stochastic frontier production function-the type introduced by Aigner, Lovell, and Schmidt (1977) and Meeusen and van den Broeck (1977). Such a production frontier model consists of a production function of the usual regression type but with an error term equal to the sum of two parts. The first part is typically assumed to be normally distributed and represents the usual statistical noise, such as luck, weather, machine breakdown, and other events beyond the control of the firm. The second part is nonpositive and represents technical inefficiencythat is, failure to produce maximal output, given the set of inputs used. Realized output is bounded from above by a frontier that includes the deterministic part of the regression, plus the part of the error representing noise; so the frontier is stochastic. There also exist socalled deterministic frontier models, whose error term contains only the nonpositive component, but we will not consider them here (e.g., see Greene 1980). Frontier models arise naturally in the problem of efficiency measurement, since one needs a bound on output to measure efficiency. A good survey of such production functions and their relationship to the measurement of productive efficiency was given by F0rsund, Lovell, and Schmidt (1980).

1,518 citations