Download or read book Maximum Likelihood Estimation for a Heavy tailed Mixture Distribution written by Philippe Dovoedo and published by . This book was released on 2019 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Finite Mixture of Skewed Distributions written by Víctor Hugo Lachos Dávila and published by Springer. This book was released on 2018-11-12 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Finite Mixture Distributions written by B. Everitt and published by Springer. This book was released on 1981-05-28 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: General introduction; Mixtures of normal distributions; Mixtures of exponential and other continuous distributions; Mixtures of discrete distributions; Miscellaneous topics.
Download or read book The Fundamentals of Heavy Tails written by Jayakrishnan Nair and published by Cambridge University Press. This book was released on 2022-06-09 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Handbook Of Heavy tailed Distributions In Asset Management And Risk Management written by Michele Leonardo Bianchi and published by World Scientific. This book was released on 2019-03-08 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Handbook of Heavy Tailed Distributions in Finance written by S.T Rachev and published by Elsevier. This book was released on 2003-03-05 with total page 707 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Maximum Likelihood Estimation in a Mixture of Two Weibull Distributions written by Thomas Joseph Mason and published by . This book was released on 1968 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Maximum Penalized Likelihood Estimation written by P.P.B. Eggermont and published by Springer Nature. This book was released on 2020-12-15 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Maximum Likelihood Estimation of the Parameters of a Mixture of Two Normal Distributions written by David Wylie Hosmer and published by . This book was released on 1971 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Maximum Likelihood Estimation for Sample Surveys written by Raymond L. Chambers and published by CRC Press. This book was released on 2012-05-02 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Maximum Likelihood Estimation for Mixtures of Two Normal Distributions written by Nathan Paul Dick and published by . This book was released on 1971 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimization Methods for Maximum Likelihood Estimation of Mixture Distribution written by Thomas M. Krischke and published by . This book was released on 1990 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Heavy Tailed and Subexponential Distributions written by Sergey Foss and published by Springer Science & Business Media. This book was released on 2013-05-21 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: Heavy-tailed probability distributions are an important component in the modeling of many stochastic systems. They are frequently used to accurately model inputs and outputs of computer and data networks and service facilities such as call centers. They are an essential for describing risk processes in finance and also for insurance premia pricing, and such distributions occur naturally in models of epidemiological spread. The class includes distributions with power law tails such as the Pareto, as well as the lognormal and certain Weibull distributions. One of the highlights of this new edition is that it includes problems at the end of each chapter. Chapter 5 is also updated to include interesting applications to queueing theory, risk, and branching processes. New results are presented in a simple, coherent and systematic way. Graduate students as well as modelers in the fields of finance, insurance, network science and environmental studies will find this book to be an essential reference.
Download or read book Maximum Likelihood Estimation of the Parameters of a Mixture of Two Gamma Distributions written by Navinchandra Tribhovandas Parikh and published by . This book was released on 1973 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Mixture Models written by Geoffrey McLachlan and published by John Wiley & Sons. This book was released on 2004-03-22 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date, comprehensive account of major issues in finitemixture modeling This volume provides an up-to-date account of the theory andapplications of modeling via finite mixture distributions. With anemphasis on the applications of mixture models in both mainstreamanalysis and other areas such as unsupervised pattern recognition,speech recognition, and medical imaging, the book describes theformulations of the finite mixture approach, details itsmethodology, discusses aspects of its implementation, andillustrates its application in many common statisticalcontexts. Major issues discussed in this book include identifiabilityproblems, actual fitting of finite mixtures through use of the EMalgorithm, properties of the maximum likelihood estimators soobtained, assessment of the number of components to be used in themixture, and the applicability of asymptotic theory in providing abasis for the solutions to some of these problems. The author alsoconsiders how the EM algorithm can be scaled to handle the fittingof mixture models to very large databases, as in data miningapplications. This comprehensive, practical guide: * Provides more than 800 references-40% published since 1995 * Includes an appendix listing available mixture software * Links statistical literature with machine learning and patternrecognition literature * Contains more than 100 helpful graphs, charts, and tables Finite Mixture Models is an important resource for both applied andtheoretical statisticians as well as for researchers in the manyareas in which finite mixture models can be used to analyze data.
Download or read book Fat Tailed Distributions written by Roger M. Cooke and published by John Wiley & Sons. This book was released on 2014-12-03 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title is written for the numerate nonspecialist, and hopes to serve three purposes. First it gathers mathematical material from diverse but related fields of order statistics, records, extreme value theory, majorization, regular variation and subexponentiality. All of these are relevant for understanding fat tails, but they are not, to our knowledge, brought together in a single source for the target readership. Proofs that give insight are included, but for most fussy calculations the reader is referred to the excellent sources referenced in the text. Multivariate extremes are not treated. This allows us to present material spread over hundreds of pages in specialist texts in twenty pages. Chapter 5 develops new material on heavy tail diagnostics and gives more mathematical detail. Since variances and covariances may not exist for heavy tailed joint distributions, Chapter 6 reviews dependence concepts for certain classes of heavy tailed joint distributions, with a view to regressing heavy tailed variables. Second, it presents a new measure of obesity. The most popular definitions in terms of regular variation and subexponentiality invoke putative properties that hold at infinity, and this complicates any empirical estimate. Each definition captures some but not all of the intuitions associated with tail heaviness. Chapter 5 studies two candidate indices of tail heaviness based on the tendency of the mean excess plot to collapse as data are aggregated. The probability that the largest value is more than twice the second largest has intuitive appeal but its estimator has very poor accuracy. The Obesity index is defined for a positive random variable X as: Ob(X) = P (X1 +X4 > X2 +X3|X1 ≤ X2 ≤ X3 ≤ X4), Xi independent copies of X. For empirical distributions, obesity is defined by bootstrapping. This index reasonably captures intuitions of tail heaviness. Among its properties, if α > 1 then Ob(X) Ob(Xα). However, it does not completely mimic the tail index of regularly varying distributions, or the extreme value index. A Weibull distribution with shape 1/4 is more obese than a Pareto distribution with tail index 1, even though this Pareto has infinite mean and the Weibull’s moments are all finite. Chapter 5 explores properties of the Obesity index. Third and most important, we hope to convince the reader that fat tail phenomena pose real problems; they are really out there and they seriously challenge our usual ways of thinking about historical averages, outliers, trends, regression coefficients and confidence bounds among many other things. Data on flood insurance claims, crop loss claims, hospital discharge bills, precipitation and damages and fatalities from natural catastrophes drive this point home. While most fat tailed distributions are ”bad”, research in fat tails is one distribution whose tail will hopefully get fatter.
Download or read book Constrained maximum likelihood estimation for a mixture of m univariate normal distributions written by Richard Joseph Hathaway and published by . This book was released on 1983 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt:
