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Famílies exponencials (Estadística) --- Distribució (Teoria de la probabilitat) --- Exponential families (Statistics) --- Families, Exponential (Statistics) --- Distribution (Probability theory)

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This book provides a compact and systematic overview of closure properties of heavy-tailed and related distributions, including closure under tail equivalence, convolution, finite mixing, maximum, minimum, convolution power and convolution roots, and product-convolution closure. It includes examples and counterexamples that give an insight into the theory and provides numerous references to technical details and proofs for a deeper study of the subject. The book will serve as a useful reference for graduate students, young researchers, and applied scientists.

Probabilities. --- Distribution (Probability theory). --- Stochastic models. --- Actuarial science. --- Applied Probability. --- Distribution Theory. --- Probability Theory. --- Stochastic Modelling in Statistics. --- Actuarial Mathematics. --- Distribució (Teoria de la probabilitat)

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This book provides an account of weak convergence theory, empirical processes, and their application to a wide variety of problems in statistics. The first part of the book presents a thorough treatment of stochastic convergence in its various forms. Part 2 brings together the theory of empirical processes in a form accessible to statisticians and probabilists. In Part 3, the authors cover a range of applications in statistics including rates of convergence of estimators; limit theorems for M− and Z−estimators; the bootstrap; the functional delta-method and semiparametric estimation. Most of the chapters conclude with “problems and complements.” Some of these are exercises to help the reader’s understanding of the material, whereas others are intended to supplement the text. This second edition includes many of the new developments in the field since publication of the first edition in 1996: Glivenko-Cantelli preservation theorems; new bounds on expectations of suprema of empirical processes; new bounds on covering numbers for various function classes; generic chaining; definitive versions of concentration bounds; and new applications in statistics including penalized M-estimation, the lasso, classification, and support vector machines. The approximately 200 additional pages also round out classical subjects, including chapters on weak convergence in Skorokhod space, on stable convergence, and on processes based on pseudo-observations.

Statistics. --- Applied Statistics. --- Statistical Theory and Methods. --- Bayesian Inference. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Processos estocàstics --- Convergència (Matemàtica) --- Distribució (Teoria de la probabilitat) --- Mostreig (Estadística)

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Probabilities. --- Mathematics. --- Math --- Science --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Probabilitats --- Càlcul de probabilitats --- Inferència estadística --- Probabilitat --- Combinatòria (Matemàtica) --- Lògica --- Lògica matemàtica --- Anàlisi de sèries temporals --- Correlació (Estadística) --- Descomposició (Matemàtica) --- Distribució (Teoria de la probabilitat) --- Fiabilitat (Enginyeria) --- Funcions característiques --- Geometria estocàstica --- Incertesa (Teoria de la informació) --- Integrals de camí --- Jocs d'atzar (Matemàtica) --- Mitjana (Estadística) --- Probabilitats combinatòries --- Processos estocàstics --- Sort --- Teoremes de límit (Teoria de probabilitats) --- Teoria matemàtica de la comunicació --- Variables aleatòries --- Atzar --- Risc (Economia) --- Teoria ergòdica

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Probabilitats --- Càlcul de probabilitats --- Inferència estadística --- Probabilitat --- Combinatòria (Matemàtica) --- Lògica --- Lògica matemàtica --- Anàlisi de sèries temporals --- Correlació (Estadística) --- Descomposició (Matemàtica) --- Distribució (Teoria de la probabilitat) --- Fiabilitat (Enginyeria) --- Funcions característiques --- Geometria estocàstica --- Incertesa (Teoria de la informació) --- Integrals de camí --- Jocs d'atzar (Matemàtica) --- Mitjana (Estadística) --- Probabilitats combinatòries --- Processos estocàstics --- Sort --- Teoremes de límit (Teoria de probabilitats) --- Teoria matemàtica de la comunicació --- Variables aleatòries --- Atzar --- Risc (Economia) --- Teoria ergòdica --- Probabilities. --- Quasisymmetric groups. --- Quasisymmetry (Group theory) --- Group theory --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk