Gatha Cognition®
Perception, Learning and Reasoning
Statistical Theory of Extremes
Statistical Theory of Extremes
Statistical Theory of Extremes

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

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
978-81-932622-3-8
dx.doi.org/10.21523/gcb1
Gatha Cognition Free Publication
Cross Referance

Preface

Preface

Part-1: Probabilistic Patterns of Univariate Statistical Extremes

Introduction
Asymptotics of Univariate Extremes
Attraction Structure and Speed of Convergence
Annex-1: On The “Duality” between Extremes and Sums
Annex-3: On the δ​​-Method
Exercises

Part-2: Statistics for Univariate Extremes

A Quick Exploration of Extreme Data
Statistical Analysis of the Gumbel Model
Statistics for Fréchet Distribution
Statistical Decision for Weibull Distribution for Minima
Analitic Statistical Choice for Univariate Extremes
Statistical Analysis With Partial Information
Annex-4
Exercises

Part-3: Multivariate Extremes

Bivariate Extremes: Probabilistic Results
Bivariate Extremes: Models and Statistical Decision
Multivariate Extremes
Annex-5: On the Quadrants Method
Exercises

Part-4: Stochastic Sequences and Processes of Extremes

Extremes in Random Sequences and Stochastic Processes
Extremal Sequences and Processes: Basics and Statistics
Other Processes of Extremes: Basics and Statistics
Annex-6: On The Choice of Stochastic Processes Models
Exercises

Part-5: Complements

GEA-General Extremes Analysis: A guide in natural language
Some Case Studies
Exercises
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