Statistical Theory of Extremes

Name: Statistical Theory of Extremes
ISBN: 978-81-932622-3-8

José Tiago de Fonseca Oliveira

doi:10.21523/gcb1

Statistical Theory of Extremes

Author :

Professor. José Tiago de Fonseca Oliveira ¹

1.Academia das Ciências de Lisboa (Lisbon Academy of Sciences), Lisbon, Portugal.

Managing Editor :

Professor. José Carlos Brandão Tiago de Oliveira

1) UNESCO Chair in Intangible Heritage and Traditional Know-how: Linking Heritage, University of Évora, Portugal ; and 2) Center of Philosophy of Science, Faculty of Sciences, University of Lisbon, Lisbon, Portugal

ISBN :

978-81-932622-3-8

DOI :

https://doi.org/10.21523/gcb1

Open Access — all chapters free to read and download Read chapters

Current Chapter

Preface

Views: 1125

Preface

Author(s) : Professor. José Tiago de Fonseca Oliveira

DOI : https://doi.org/10.21523/gcb1.1701

Pages : I-III

Date of Publication : 23-06-2017

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Part-1: Probabilistic Patterns of Univariate Statistical Extremes

Views: 1175

Introduction

Author(s) : Professor. José Tiago de Fonseca Oliveira

DOI : https://doi.org/10.21523/gcb1.1702

Pages : 1-10

Date of Publication : 23-06-2017

Keywords : Asymptotic behaviours,Asymptotic distribution,Exceedances,Order statistics,Weibull distribution,Stochastic Model,Experimental digression

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Views: 1286

Asymptotics of Univariate Extremes

Author(s) : Professor. José Tiago de Fonseca Oliveira

DOI : https://doi.org/10.21523/gcb1.1703

Pages : 11-44

Date of Publication : 23-06-2017

Keywords : Weibull distributions,Fréchet distributions,Gumbel distributions,Max-stability,LLN for extremes

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Views: 2402

Attraction Structure and Speed of Convergence

Author(s) : Professor. José Tiago de Fonseca Oliveira

DOI : https://doi.org/10.21523/gcb1.1704

Pages : 45-62

Date of Publication : 23-06-2017

Keywords : Tail equivalent,Slow variation,Quantile function,Speed of convergence,Attraction coefficients

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Views: 1569

Annex-1: On The “Duality” between Extremes and Sums

Author(s) : Professor. José Tiago de Fonseca Oliveira

DOI : https://doi.org/10.21523/gcb1.1705

Pages : 63-64

Date of Publication : 23-06-2017

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Views: 1484

Annex-2: On the Khintchine’s Convergence of Types Theorem

Author(s) : Professor. José Tiago de Fonseca Oliveira

DOI : https://doi.org/10.21523/gcb1.1706

Pages : 65-66

Date of Publication : 23-06-2017

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Views: 1463

Annex-3: On the δ-Method

Author(s) : Professor. José Tiago de Fonseca Oliveira

DOI : https://doi.org/10.21523/gcb1.1707

Pages : 67-69

Date of Publication : 23-06-2017

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Views: 1606

Exercises

Author(s) : Professor. José Tiago de Fonseca Oliveira

DOI : https://doi.org/10.21523/gcb1.1708

Pages : 70-77

Date of Publication : 23-06-2017

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Part-2: Statistics for Univariate Extremes

Views: 1627

A Quick Exploration of Extreme Data

Author(s) : Professor. José Tiago de Fonseca Oliveira

DOI : https://doi.org/10.21523/gcb1.1709

Pages : 78-92

Date of Publication : 23-06-2017

Keywords : Extreme values trilemma,Probability paper,Statistical choice

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Views: 2118

Statistical Analysis of the Gumbel Model

Author(s) : Professor. José Tiago de Fonseca Oliveira

DOI : https://doi.org/10.21523/gcb1.1710

Pages : 93-120

Date of Publication : 23-06-2017

Keywords : Tolerance intervals,Test of hypotheses,BLIE,ME,MLE,Statistical inference

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Views: 1476

Statistics for Fréchet Distribution

Author(s) : Professor. José Tiago de Fonseca Oliveira

DOI : https://doi.org/10.21523/gcb1.1711

Pages : 121-129

Date of Publication : 23-06-2017

Keywords : Fréchet distribution of maxima,Location and dispersion parameters,Weibull distribution of minima,Moment generating function,Estimation, testing, and point prediction,MLE,Confidence region

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Views: 1538

Statistical Decision for Weibull Distribution for Minima

Author(s) : Professor. José Tiago de Fonseca Oliveira

DOI : https://doi.org/10.21523/gcb1.1712

Pages : 130-157

Date of Publication : 23-06-2017

Keywords : Weibull distribution,Minima,Point prediction,Time-to-failure

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Views: 1458

Analitic Statistical Choice for Univariate Extremes

Author(s) : Professor. José Tiago de Fonseca Oliveira

DOI : https://doi.org/10.21523/gcb1.1713

Pages : 158-173

Date of Publication : 23-06-2017

Keywords : Weibull distribution,Gumbel distribution,Fréchet distribution,Locally optimal approach,Variational approach

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Views: 1703

Statistical Analysis With Partial Information

Author(s) : Professor. José Tiago de Fonseca Oliveira

DOI : https://doi.org/10.21523/gcb1.1714

Pages : 174-200

Date of Publication : 23-06-2017

Keywords : Extreme observations,Lower tail,Subsample method,Largest observations,Subsample maxima,Bock partitions

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Views: 1520

Annex-4

Author(s) : Professor. José Tiago de Fonseca Oliveira

DOI : https://doi.org/10.21523/gcb1.1715

Pages : 201-219

Date of Publication : 23-06-2017

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Views: 2238

Exercises

Author(s) : Professor. José Tiago de Fonseca Oliveira

DOI : https://doi.org/10.21523/gcb1.1716

Pages : 220-228

Date of Publication : 23-06-2017

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Part-3: Multivariate Extremes

Views: 1583

Bivariate Extremes: Probabilistic Results

Author(s) : Professor. José Tiago de Fonseca Oliveira

DOI : https://doi.org/10.21523/gcb1.1717

Pages : 229-268

Date of Publication : 23-06-2017

Keywords : Bivariate asymptotic distributions,Univariate extremes,Correlation,Regression,Bivariate reduced extremes

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Views: 1575

Bivariate Extremes: Models and Statistical Decision

Author(s) : Professor. José Tiago de Fonseca Oliveira

DOI : https://doi.org/10.21523/gcb1.1718

Pages : 269-300

Date of Publication : 23-06-2017

Keywords : Statistical decision,Asymptotic approximation,Samples,Differentiable models,Logistic modes

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Views: 1658

Multivariate Extremes

Author(s) : Professor. José Tiago de Fonseca Oliveira

DOI : https://doi.org/10.21523/gcb1.1719

Pages : 301-310

Date of Publication : 23-06-2017

Keywords : Bivariate models,Correlation coefficients,Linear regression,Multivariate extreme distribution,Prosbabilistic theory,Variance

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Views: 1518

Annex-5: On the Quadrants Method

Author(s) : Professor. José Tiago de Fonseca Oliveira

DOI : https://doi.org/10.21523/gcb1.1720

Pages : 311-312

Date of Publication : 23-06-2017

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Views: 1646

Exercises

Author(s) : Professor. José Tiago de Fonseca Oliveira

DOI : https://doi.org/10.21523/gcb1.1721

Pages : 313-318

Date of Publication : 23-06-2017

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Part-4: Stochastic Sequences and Processes of Extremes

Views: 2038

Extremes in Random Sequences and Stochastic Processes

Author(s) : Professor. José Tiago de Fonseca Oliveira

DOI : https://doi.org/10.21523/gcb1.1722

Pages : 319-332

Date of Publication : 23-06-2017

Keywords : Global extremes,Local extremes,Wiener-Lévy processes,Gaussian stationary processes,Stochastic processes,Random sequence

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Views: 1709

Extremal Sequences and Processes: Basics and Statistics

Author(s) : Professor. José Tiago de Fonseca Oliveira

DOI : https://doi.org/10.21523/gcb1.1723

Pages : 333-353

Date of Publication : 23-06-2017

Keywords : Extremal sequences,Extremal processes,Maxima,Independent extremes,Limiting characterizations,Parameterization,Ergodic theorem

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Views: 1542

Other Processes of Extremes: Basics and Statistics

Author(s) : Professor. José Tiago de Fonseca Oliveira

DOI : https://doi.org/10.21523/gcb1.17024

Pages : 354-379

Date of Publication : 23-06-2017

Keywords : Extremes,Extreme-Markovian-stationary,Normal-Markovian-stationary,Sliding extreme (SE) sequences,Statistical decision

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Views: 1528

Annex-6: On The Choice of Stochastic Processes Models

Author(s) : Professor. José Tiago de Fonseca Oliveira

DOI : https://doi.org/10.21523/gcb1.17025

Pages : 380-381

Date of Publication : 23-06-2017

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Views: 1060

Exercises

Author(s) : Professor. José Tiago de Fonseca Oliveira

DOI : https://doi.org/10.21523/gcb1.17026

Pages : 382-384

Date of Publication : 23-06-2017

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Part-5: Complements

Views: 1575

GEA-General Extremes Analysis: A guide in natural language

Author(s) : Professor. José Tiago de Fonseca Oliveira

DOI : https://doi.org/10.21523/gcb1.1727

Pages : 385-389

Date of Publication : 23-06-2017

Keywords : Non-diagram fluxogram,Statistical Choice of Model,Multivariate Model,Stochastic processes

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Views: 1562

Some Case Studies

Author(s) : Professor. José Tiago de Fonseca Oliveira

DOI : https://doi.org/10.21523/gcb1.1728

Pages : 390-399

Date of Publication : 23-06-2017

Keywords : Univariate extremes data,Multivariate extremes data,Multivariate extremes,Exceedance probabilities

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Views: 1190

Exercises

Author(s) : Professor. José Tiago de Fonseca Oliveira

DOI : https://doi.org/10.21523/gcb1.1729

Pages : 400-401

Date of Publication : 23-06-2017

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Statistical Theory of Extremes - Gatha Cognition

Preface

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Part-1: Probabilistic Patterns of Univariate Statistical Extremes

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Part-2: Statistics for Univariate Extremes

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Part-3: Multivariate Extremes

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Part-4: Stochastic Sequences and Processes of Extremes

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Part-5: Complements

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