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Fitting The Convolution Of Negative Binomial And Poisson Distributions On Data
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Book Synopsis Recursions for Convolutions and Compound Distributions with Insurance Applications by : Bjoern Sundt
Download or read book Recursions for Convolutions and Compound Distributions with Insurance Applications written by Bjoern Sundt and published by Springer Science & Business Media. This book was released on 2009-04-21 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since 1980, methods for recursive evaluation of aggregate claims distributions have received extensive attention in the actuarial literature. This book gives a unified survey of the theory and is intended to be self-contained to a large extent. As the methodology is applicable also outside the actuarial field, it is presented in a general setting, but actuarial applications are used for motivation. The book is divided into two parts. Part I is devoted to univariate distributions, whereas in Part II, the methodology is extended to multivariate settings. Primarily intended as a monograph, this book can also be used as text for courses on the graduate level. Suggested outlines for such courses are given. The book is of interest for actuaries and statisticians working within the insurance and finance industry, as well as for people in other fields like operations research and reliability theory.
Book Synopsis Univariate Discrete Distributions by : Norman L. Johnson
Download or read book Univariate Discrete Distributions written by Norman L. Johnson and published by John Wiley & Sons. This book was released on 2005-08-30 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Set Contains: Continuous Multivariate Distributions, Volume 1, Models and Applications, 2nd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Continuous Univariate Distributions, Volume 1, 2nd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Continuous Univariate Distributions, Volume 2, 2nd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Discrete Multivariate Distributions by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Univariate Discrete Distributions, 3rd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Discover the latest advances in discrete distributions theory The Third Edition of the critically acclaimed Univariate Discrete Distributions provides a self-contained, systematic treatment of the theory, derivation, and application of probability distributions for count data. Generalized zeta-function and q-series distributions have been added and are covered in detail. New families of distributions, including Lagrangian-type distributions, are integrated into this thoroughly revised and updated text. Additional applications of univariate discrete distributions are explored to demonstrate the flexibility of this powerful method. A thorough survey of recent statistical literature draws attention to many new distributions and results for the classical distributions. Approximately 450 new references along with several new sections are introduced to reflect the current literature and knowledge of discrete distributions. Beginning with mathematical, probability, and statistical fundamentals, the authors provide clear coverage of the key topics in the field, including: Families of discrete distributions Binomial distribution Poisson distribution Negative binomial distribution Hypergeometric distributions Logarithmic and Lagrangian distributions Mixture distributions Stopped-sum distributions Matching, occupancy, runs, and q-series distributions Parametric regression models and miscellanea Emphasis continues to be placed on the increasing relevance of Bayesian inference to discrete distribution, especially with regard to the binomial and Poisson distributions. New derivations of discrete distributions via stochastic processes and random walks are introduced without unnecessarily complex discussions of stochastic processes. Throughout the Third Edition, extensive information has been added to reflect the new role of computer-based applications. With its thorough coverage and balanced presentation of theory and application, this is an excellent and essential reference for statisticians and mathematicians.
Book Synopsis Soft Multihadron Dynamics by : W. Kittel
Download or read book Soft Multihadron Dynamics written by W. Kittel and published by World Scientific. This book was released on 2005 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a comprehensive account of the development and present status of the field of soft (i.e. non-perturbative) phenomena encountered in the production of (multi-) hadronic final states by the collision of various types of particles at high energies. Phenomenological models used to describe the data are in general inspired by Quantum Chromo Dynamics (QCD) and the book repeatedly crosses the border OCo if at all existent OCo between soft (non-perturbative) and hard (perturbative) QCD."
Book Synopsis An Introduction to Discrete-Valued Time Series by : Christian H. Weiss
Download or read book An Introduction to Discrete-Valued Time Series written by Christian H. Weiss and published by John Wiley & Sons. This book was released on 2018-02-05 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: A much-needed introduction to the field of discrete-valued time series, with a focus on count-data time series Time series analysis is an essential tool in a wide array of fields, including business, economics, computer science, epidemiology, finance, manufacturing and meteorology, to name just a few. Despite growing interest in discrete-valued time series—especially those arising from counting specific objects or events at specified times—most books on time series give short shrift to that increasingly important subject area. This book seeks to rectify that state of affairs by providing a much needed introduction to discrete-valued time series, with particular focus on count-data time series. The main focus of this book is on modeling. Throughout numerous examples are provided illustrating models currently used in discrete-valued time series applications. Statistical process control, including various control charts (such as cumulative sum control charts), and performance evaluation are treated at length. Classic approaches like ARMA models and the Box-Jenkins program are also featured with the basics of these approaches summarized in an Appendix. In addition, data examples, with all relevant R code, are available on a companion website. Provides a balanced presentation of theory and practice, exploring both categorical and integer-valued series Covers common models for time series of counts as well as for categorical time series, and works out their most important stochastic properties Addresses statistical approaches for analyzing discrete-valued time series and illustrates their implementation with numerous data examples Covers classical approaches such as ARMA models, Box-Jenkins program and how to generate functions Includes dataset examples with all necessary R code provided on a companion website An Introduction to Discrete-Valued Time Series is a valuable working resource for researchers and practitioners in a broad range of fields, including statistics, data science, machine learning, and engineering. It will also be of interest to postgraduate students in statistics, mathematics and economics.
Book Synopsis Bivariate Discrete Distributions by : Kocherlakota
Download or read book Bivariate Discrete Distributions written by Kocherlakota and published by CRC Press. This book was released on 2017-11-22 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This useful reference/text provides a comprehensive study of the various bivariate discretedistributions that have appeared in the literature- written in an accessible manner thatassumes no more than a first course in mathematical statistics.Supplying individualized treatment of topics while simultaneously exploiting the interrelationshipsof the material, Bivariate Discrete Distributions details the latest techniques ofcomputer simulation for the distributions considered ... contains a general introduction tothe structural properties of discrete distributions, including generating functions, momentrelationships, and the basic ideas of generalizing . . . develops distributions using samplingschemes . .. explores the role of compounding ... covers Waring and "short" distributionsfor use in accident theory ... discusses problems of statistical inference, emphasizing techniquespertinent to the discrete case ... and much more!Containing over 1000 helpful equations, Bivariate Discrete Distributions is
Book Synopsis Insurance Abstracts and Reviews by :
Download or read book Insurance Abstracts and Reviews written by and published by . This book was released on 1987 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Loss Data Analysis written by Henryk Gzyl and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-03-06 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with two complementary topics. On one hand the book deals with the problem of determining the the probability distribution of a positive compound random variable, a problem which appears in the banking and insurance industries, in many areas of operational research and in reliability problems in the engineering sciences. On the other hand, the methodology proposed to solve such problems, which is based on an application of the maximum entropy method to invert the Laplace transform of the distributions, can be applied to many other problems. The book contains applications to a large variety of problems, including the problem of dependence of the sample data used to estimate empirically the Laplace transform of the random variable. Contents Introduction Frequency models Individual severity models Some detailed examples Some traditional approaches to the aggregation problem Laplace transforms and fractional moment problems The standard maximum entropy method Extensions of the method of maximum entropy Superresolution in maxentropic Laplace transform inversion Sample data dependence Disentangling frequencies and decompounding losses Computations using the maxentropic density Review of statistical procedures
Book Synopsis Applied Econometrics with SAS by : Barry K. Goodwin
Download or read book Applied Econometrics with SAS written by Barry K. Goodwin and published by SAS Institute. This book was released on 2018-04-04 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using Applied Econometrics with SAS: Modeling Demand, Supply, and Risk, you will quickly master SAS applications for implementing and estimating standard models in the field of econometrics. This guide introduces you to the major theories underpinning applied demand and production economics. For each of its three main topics—demand, supply, and risk—a concise theoretical orientation leads directly into consideration of specific economic models and econometric techniques, collectively covering the following: Double-log demand systems Linear expenditure systems Almost ideal demand systems Rotterdam models Random parameters logit demand models Frequency-severity models Compound distribution models Cobb-Douglas production functions Translogarithmic cost functions Generalized Leontief cost functions Density estimation techniques Copula models SAS procedures that facilitate estimation of demand, supply, and risk models include the following, among others: PROC MODEL PROC COPULA PROC SEVERITY PROC KDE PROC LOGISTIC PROC HPCDM PROC IML PROC REG PROC COUNTREG PROC QLIM An empirical example, SAS programming code, and a complete data set accompany each econometric model, empowering you to practice these techniques while reading. Examples are drawn from both major scholarly studies and business applications so that professors, graduate students, government economic researchers, agricultural analysts, actuaries, and underwriters, among others, will immediately benefit. This book is part of the SAS Press program.
Book Synopsis Fitting of Data by Generalized Poisson Distributions and Some Tests of Hypotheses by : Paul Norman Hinz
Download or read book Fitting of Data by Generalized Poisson Distributions and Some Tests of Hypotheses written by Paul Norman Hinz and published by . This book was released on 1967 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Combinatorial Methods in Discrete Distributions by : Charalambos A. Charalambides
Download or read book Combinatorial Methods in Discrete Distributions written by Charalambos A. Charalambides and published by John Wiley & Sons. This book was released on 2005-06-24 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique approach illustrating discrete distribution theory through combinatorial methods This book provides a unique approach by presenting combinatorial methods in tandem with discrete distribution theory. This method, particular to discreteness, allows readers to gain a deeper understanding of theory by using applications to solve problems. The author makes extensive use of the reduction approach to conditional distributions of independent random occupancy numbers, and provides excellent studies of occupancy and sequential occupancy distributions, convolutions of truncated discrete distributions, and compound and mixture distributions. Combinatorial Methods in Discrete Distributions begins with a brief presentation of set theory followed by basic counting principles. Fundamental principles of combinatorics, finite differences, and discrete probability are included to give readers the necessary foundation to the topics presented in the text. A thorough examination of the field is provided and features: Stirling numbers and generalized factorial coefficients Occupancy and sequential occupancy distributions n-fold convolutions of truncated distributions Compound and mixture distributions Thoroughly worked examples aid readers in understanding complex theory and discovering how theory can be applied to solve practical problems. An appendix with hints and answers to the exercises helps readers work through the more complex sections. Reference notes are provided at the end of each chapter, and an extensive bibliography offers readers a resource for additional information on specialized topics.
Book Synopsis Computation and Modelling in Insurance and Finance by : Erik Bølviken
Download or read book Computation and Modelling in Insurance and Finance written by Erik Bølviken and published by Cambridge University Press. This book was released on 2014-04-10 with total page 713 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on what actuaries need in practice, this introductory account provides readers with essential tools for handling complex problems and explains how simulation models can be created, used and re-used (with modifications) in related situations. The book begins by outlining the basic tools of modelling and simulation, including a discussion of the Monte Carlo method and its use. Part II deals with general insurance and Part III with life insurance and financial risk. Algorithms that can be implemented on any programming platform are spread throughout and a program library written in R is included. Numerous figures and experiments with R-code illustrate the text. The author's non-technical approach is ideal for graduate students, the only prerequisites being introductory courses in calculus and linear algebra, probability and statistics. The book will also be of value to actuaries and other analysts in the industry looking to update their skills.
Download or read book ASTIN Bulletin written by and published by . This book was released on 1988 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Reliability Data Analysis with Excel and Minitab by : Kenneth S. Stephens
Download or read book Reliability Data Analysis with Excel and Minitab written by Kenneth S. Stephens and published by Quality Press. This book was released on 2011-08-30 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many reliability engineers are gainfully employed in considerations of the physical nature of components and systems-bringing to bear theories and methodologies of physics, electronics, mechanics, material science, chemistry, and so on. But when a product has been designed and manufactured, its performance in terms of durability, strength, and life become a matter of test, measurement, and analysis. Statistical theories and methodologies provide a large number of analytical tools to assist the reliability engineer in studying the performance of products and the fruits of the physical considerations, even revealing further improvements that can be made in the physical properties. Hence, reliability is a multidisciplined field of endeavor. Statistical theories and methodologies allow estimation of important characteristics as well as levels of confidence or assurance (or lack thereof) with respect to the estimations. They also provide direction in actions necessary to improve estimates and confidence levels if results are too variable to render important decisions. Some derivations are contained in this text, but the approach here is meant to be more practical, in following each topic introduced and expanded with examples. On each topic covered, reasonably practical examples are used to illustrate and demonstrate the procedures introduced and discussed. For all of these examples either Excel files or Minitab files or both have been prepared (available from Quality Press). They can be readily accessed and opened directly in their respective software packages to permit the preparation of new files specifically for use by the reader. "This book provides a much-needed theoretical text to aid advanced reliability engineering data analysis. Applications using Excel and Minitab support a broad span of probability applications for reliability data analysts. I most strongly recommend this book for seasoned Six Sigma Black Belts or statisticians who must support Design for Six Sigma applications for new product development projects. It's rich in food for thought as well as providing a most nourishing banquet for consumption by engineers --- it is not for light reading as a snack, but it must be consumed as a seven-course meal!" Gregory H. Watson Chairman, International Academy for Quality ASQ Past-President and Fellow
Book Synopsis Asymptotic Expansions of Integrals by : Norman Bleistein
Download or read book Asymptotic Expansions of Integrals written by Norman Bleistein and published by Courier Corporation. This book was released on 1986-01-01 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excellent introductory text, written by two experts, presents a coherent and systematic view of principles and methods. Topics include integration by parts, Watson's lemma, LaPlace's method, stationary phase, and steepest descents. Additional subjects include the Mellin transform method and less elementary aspects of the method of steepest descents. 1975 edition.
Book Synopsis Statistical Analysis of Extreme Values by : Rolf-Dieter Reiss
Download or read book Statistical Analysis of Extreme Values written by Rolf-Dieter Reiss and published by Springer Science & Business Media. This book was released on 2007-06-21 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a self-contained introduction to parametric modeling, exploratory analysis and statistical interference for extreme values, as used in disciplines from hydrology to finance to environmental science. Updated and expanded by 100 pages.
Book Synopsis Operational Risk by : Harry H. Panjer
Download or read book Operational Risk written by Harry H. Panjer and published by John Wiley & Sons. This book was released on 2006-07-28 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover how to optimize business strategies from both qualitative and quantitative points of view Operational Risk: Modeling Analytics is organized around the principle that the analysis of operational risk consists, in part, of the collection of data and the building of mathematical models to describe risk. This book is designed to provide risk analysts with a framework of the mathematical models and methods used in the measurement and modeling of operational risk in both the banking and insurance sectors. Beginning with a foundation for operational risk modeling and a focus on the modeling process, the book flows logically to discussion of probabilistic tools for operational risk modeling and statistical methods for calibrating models of operational risk. Exercises are included in chapters involving numerical computations for students' practice and reinforcement of concepts. Written by Harry Panjer, one of the foremost authorities in the world on risk modeling and its effects in business management, this is the first comprehensive book dedicated to the quantitative assessment of operational risk using the tools of probability, statistics, and actuarial science. In addition to providing great detail of the many probabilistic and statistical methods used in operational risk, this book features: * Ample exercises to further elucidate the concepts in the text * Definitive coverage of distribution functions and related concepts * Models for the size of losses * Models for frequency of loss * Aggregate loss modeling * Extreme value modeling * Dependency modeling using copulas * Statistical methods in model selection and calibration Assuming no previous expertise in either operational risk terminology or in mathematical statistics, the text is designed for beginning graduate-level courses on risk and operational management or enterprise risk management. This book is also useful as a reference for practitioners in both enterprise risk management and risk and operational management.
Book Synopsis Advanced State Space Methods for Neural and Clinical Data by : Zhe Chen
Download or read book Advanced State Space Methods for Neural and Clinical Data written by Zhe Chen and published by Cambridge University Press. This book was released on 2015-10-15 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: This authoritative work provides an in-depth treatment of state space methods, with a range of applications in neural and clinical data. Advanced and state-of-the-art research topics are detailed, including topics in state space analyses, maximum likelihood methods, variational Bayes, sequential Monte Carlo, Markov chain Monte Carlo, nonparametric Bayesian, and deep learning methods. Details are provided on practical applications in neural and clinical data, whether this is characterising time series data from neural spike trains recorded from the rat hippocampus, the primate motor cortex, or the human EEG, MEG or fMRI, or physiological measurements of heartbeats or blood pressures. With real-world case studies of neuroscience experiments and clinical data sets, and written by expert authors from across the field, this is an ideal resource for anyone working in neuroscience and physiological data analysis.
