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Author: Philippe Dovoedo Publisher: ISBN: 9781088332948 Category : Statistics Languages : en Pages : 99
Book Description
In an increasingly connected global environment, "high-impact, low-probability" (HILP) events can have devastating consequences and result in large insurance losses with a heavy- tailed distribution. Examples of such events include Hurricane Katrina, the Deepwater Horizon oil disaster and the Japanese nuclear crisis and tsunami. According to the 2012 Blackett Review of HILP Risks from the UK Government Office for Science, the identification of low-probability risks, and the subsequent development of mitigation plans, is complicated by their rare or conjectural nature, and their potential for causing impacts beyond everyday experience. Extremal mixture models and more generally extreme value analysis help assess HILP risks. In this dissertation, we introduce various classes of heavy-tailed distributions before moving on to mixture models. In particular, we are interested in the mixture of a heavy-tailed distribution and a light-tailed distribution. Estimation of the mixture distribution is based on the expectation-maximization (EM) algorithm and model selection is achieved using information criteria. Our results indicate that one of the components of our mixture may provide us with a good model for modeling nonnegative, heavy-tailed data.
Author: Philippe Dovoedo Publisher: ISBN: 9781088332948 Category : Statistics Languages : en Pages : 99
Book Description
In an increasingly connected global environment, "high-impact, low-probability" (HILP) events can have devastating consequences and result in large insurance losses with a heavy- tailed distribution. Examples of such events include Hurricane Katrina, the Deepwater Horizon oil disaster and the Japanese nuclear crisis and tsunami. According to the 2012 Blackett Review of HILP Risks from the UK Government Office for Science, the identification of low-probability risks, and the subsequent development of mitigation plans, is complicated by their rare or conjectural nature, and their potential for causing impacts beyond everyday experience. Extremal mixture models and more generally extreme value analysis help assess HILP risks. In this dissertation, we introduce various classes of heavy-tailed distributions before moving on to mixture models. In particular, we are interested in the mixture of a heavy-tailed distribution and a light-tailed distribution. Estimation of the mixture distribution is based on the expectation-maximization (EM) algorithm and model selection is achieved using information criteria. Our results indicate that one of the components of our mixture may provide us with a good model for modeling nonnegative, heavy-tailed data.
Author: Víctor Hugo Lachos Dávila Publisher: Springer ISBN: 3319980297 Category : Mathematics Languages : en Pages : 101
Book Description
This book presents recent results in finite mixtures of skewed distributions to prepare readers to undertake mixture models using scale mixtures of skew normal distributions (SMSN). For this purpose, the authors consider maximum likelihood estimation for univariate and multivariate finite mixtures where components are members of the flexible class of SMSN distributions. This subclass includes the entire family of normal independent distributions, also known as scale mixtures of normal distributions (SMN), as well as the skew-normal and skewed versions of some other classical symmetric distributions: the skew-t (ST), the skew-slash (SSL) and the skew-contaminated normal (SCN), for example. These distributions have heavier tails than the typical normal one, and thus they seem to be a reasonable choice for robust inference. The proposed EM-type algorithm and methods are implemented in the R package mixsmsn, highlighting the applicability of the techniques presented in the book. This work is a useful reference guide for researchers analyzing heterogeneous data, as well as a textbook for a graduate-level course in mixture models. The tools presented in the book make complex techniques accessible to applied researchers without the advanced mathematical background and will have broad applications in fields like medicine, biology, engineering, economic, geology and chemistry.
Author: B. Everitt Publisher: Springer ISBN: Category : Juvenile Nonfiction Languages : en Pages : 168
Book Description
General introduction; Mixtures of normal distributions; Mixtures of exponential and other continuous distributions; Mixtures of discrete distributions; Miscellaneous topics.
Author: Jayakrishnan Nair Publisher: Cambridge University Press ISBN: 1009062964 Category : Mathematics Languages : en Pages : 266
Book Description
Heavy tails –extreme events or values more common than expected –emerge everywhere: the economy, natural events, and social and information networks are just a few examples. Yet after decades of progress, they are still treated as mysterious, surprising, and even controversial, primarily because the necessary mathematical models and statistical methods are not widely known. This book, for the first time, provides a rigorous introduction to heavy-tailed distributions accessible to anyone who knows elementary probability. It tackles and tames the zoo of terminology for models and properties, demystifying topics such as the generalized central limit theorem and regular variation. It tracks the natural emergence of heavy-tailed distributions from a wide variety of general processes, building intuition. And it reveals the controversy surrounding heavy tails to be the result of flawed statistics, then equips readers to identify and estimate with confidence. Over 100 exercises complete this engaging package.
Author: Michele Leonardo Bianchi Publisher: World Scientific ISBN: 9813276215 Category : Business & Economics Languages : en Pages : 598
Book Description
The study of heavy-tailed distributions allows researchers to represent phenomena that occasionally exhibit very large deviations from the mean. The dynamics underlying these phenomena is an interesting theoretical subject, but the study of their statistical properties is in itself a very useful endeavor from the point of view of managing assets and controlling risk. In this book, the authors are primarily concerned with the statistical properties of heavy-tailed distributions and with the processes that exhibit jumps. A detailed overview with a Matlab implementation of heavy-tailed models applied in asset management and risk managements is presented. The book is not intended as a theoretical treatise on probability or statistics, but as a tool to understand the main concepts regarding heavy-tailed random variables and processes as applied to real-world applications in finance. Accordingly, the authors review approaches and methodologies whose realization will be useful for developing new methods for forecasting of financial variables where extreme events are not treated as anomalies, but as intrinsic parts of the economic process.
Author: S.T Rachev Publisher: Elsevier ISBN: 0080557732 Category : Business & Economics Languages : en Pages : 707
Book Description
The Handbooks in Finance are intended to be a definitive source for comprehensive and accessible information in the field of finance. Each individual volume in the series should present an accurate self-contained survey of a sub-field of finance, suitable for use by finance and economics professors and lecturers, professional researchers, graduate students and as a teaching supplement. The goal is to have a broad group of outstanding volumes in various areas of finance. The Handbook of Heavy Tailed Distributions in Finance is the first handbook to be published in this series. This volume presents current research focusing on heavy tailed distributions in finance. The contributions cover methodological issues, i.e., probabilistic, statistical and econometric modelling under non- Gaussian assumptions, as well as the applications of the stable and other non -Gaussian models in finance and risk management.
Author: P.P.B. Eggermont Publisher: Springer Nature ISBN: 1071612441 Category : Mathematics Languages : en Pages : 514
Book Description
This book deals with parametric and nonparametric density estimation from the maximum (penalized) likelihood point of view, including estimation under constraints. The focal points are existence and uniqueness of the estimators, almost sure convergence rates for the L1 error, and data-driven smoothing parameter selection methods, including their practical performance. The reader will gain insight into technical tools from probability theory and applied mathematics.
Author: Raymond L. Chambers Publisher: CRC Press ISBN: 1420011359 Category : Mathematics Languages : en Pages : 374
Book Description
Sample surveys provide data used by researchers in a large range of disciplines to analyze important relationships using well-established and widely used likelihood methods. The methods used to select samples often result in the sample differing in important ways from the target population and standard application of likelihood methods can lead to
Author: Philippe Dovoedo
Author: Philippe Dovoedo
Author: Víctor Hugo Lachos Dávila
Author: B. Everitt
Author: Jayakrishnan Nair
Author: Michele Leonardo Bianchi
Author: S.T Rachev
Author: Thomas Joseph Mason
Author: Jayakrishnan Nair
Author: P.P.B. Eggermont
Author: Raymond L. Chambers