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Author : Matti Ruohonen
Publisher :
ISBN 13 : 9789516423237
Total Pages : pages
Book Rating : 4.4/5 (232 download)
Download or read book Fitting the Convolution of Negative Binomial and Poisson Distributions on Data written by Matti Ruohonen and published by . This book was released on 1983 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : C.I. BLISS
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (77 download)
Download or read book Fitting the negative binomial distribution to biological data written by C.I. BLISS and published by . This book was released on 1953 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Chester Ittner Bliss
Publisher :
ISBN 13 :
Total Pages : 25 pages
Book Rating : 4.:/5 (33 download)
Download or read book Fitting the Negative Binomial Distribution to Biological Data written by Chester Ittner Bliss and published by . This book was released on 1973 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bjoern Sundt
Publisher : Springer Science & Business Media
ISBN 13 : 3540929002
Total Pages : 348 pages
Book Rating : 4.5/5 (49 download)
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.
Author : Amanda L. Golbeck
Publisher :
ISBN 13 :
Total Pages : 154 pages
Book Rating : 4.:/5 (34 download)
Download or read book A Negative Binomial Mixture Model Solution to a Birth Distribution Problem written by Amanda L. Golbeck and published by . This book was released on 1979 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Norman L. Johnson
Publisher : John Wiley & Sons
ISBN 13 : 0471272469
Total Pages : 690 pages
Book Rating : 4.4/5 (712 download)
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.
Author : W. Kittel
Publisher : World Scientific
ISBN 13 : 9812701141
Total Pages : 672 pages
Book Rating : 4.8/5 (127 download)
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."
Author : Christian H. Weiss
Publisher : John Wiley & Sons
ISBN 13 : 1119096960
Total Pages : 300 pages
Book Rating : 4.1/5 (19 download)
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.
Author : Giovanni De Luca
Publisher : Springer Nature
ISBN 13 : 3030425800
Total Pages : 84 pages
Book Rating : 4.0/5 (34 download)
Download or read book Statistical Analysis of Operational Risk Data written by Giovanni De Luca and published by Springer Nature. This book was released on 2020-02-24 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise book for practitioners presents the statistical analysis of operational risk, which is considered the most relevant source of bank risk, after market and credit risk. The book shows that a careful statistical analysis can improve the results of the popular loss distribution approach. The authors identify the risk classes by applying a pooling rule based on statistical tests of goodness-of-fit, use the theory of the mixture of distributions to analyze the loss severities, and apply copula functions for risk class aggregation. Lastly, they assess operational risk data in order to estimate the so-called capital-at-risk that represents the minimum capital requirement that a bank has to hold. The book is primarily intended for quantitative analysts and risk managers, but also appeals to graduate students and researchers interested in bank risks.
Author : Kocherlakota
Publisher : CRC Press
ISBN 13 : 1351463462
Total Pages : 384 pages
Book Rating : 4.3/5 (514 download)
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
Author : Paul Norman Hinz
Publisher :
ISBN 13 :
Total Pages : 384 pages
Book Rating : 4.:/5 (89 download)
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:
Author : Henryk Gzyl
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3111048187
Total Pages : 222 pages
Book Rating : 4.1/5 (11 download)
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
Author : Jeffrey Monroe Miller
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (66 download)
Download or read book Comparing Poisson, Hurdle, and ZIP Model Fit Under Varying Degrees of Skew and Zero-inflation written by Jeffrey Monroe Miller and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: ABSTRACT: Many datasets are characterized as count data with a preponderance of zeros. Such data are often analyzed by ignoring the zero-inflation and assuming a Poisson distribution. The Hurdle model is more sophisticated in that it considers the zeros to be completely separate from the nonzeros. The zero-inflated Poisson (ZIP) model is similar to the Hurdle model; however, it permits some of the zeros to be analyzed along with the nonzeros. Both models, as well as the Poisson, have negative binomial formulations for use when the Poisson assumption of an equal mean and variance is violated. The choice between the models should be guided by the researcher's beliefs about the source of the zeros. Beyond this substantive concern, the choice should be based on the model providing the closest fit between the observed and predicted values. Unfortunately, the literature presents anomalous findings in terms of model superiority. Datasets with zero-inflation may vary in terms of the proportion of zeros. They may also vary in terms of the distribution for the nonzeros. Our study used a Monte Carlo design to sample 1,000 cases from positively skewed, normal, and negatively skewed distributions with proportions of zeros of .10, .25, .50, .75, and .90. The data were analyzed with each model over 2,000 simulations. The deviance statistic and Akaike's Information Criterion (AIC) value were used to compare the fit between models. Results suggest that the literature is not entirely anomalous; however, the accuracy of the findings depends on the proportion of zeros and the distribution for the nonzeros. Although the Hurdle model tends to be the superior model, there are situations when others, including the negative binomial Poisson model, are superior. The findings suggest that the researcher should consider the proportion of zeros and the distribution for the nonzeros when selecting a model to accommodate zero-inflated data.
Author :
Publisher :
ISBN 13 :
Total Pages : 498 pages
Book Rating : 4.3/5 (91 download)
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:
Author : Edward Furman
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book On the Convolution of the Negative Binomial Random Variables written by Edward Furman and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this note we are concerned with the sums S = Y1, Y2, Yn, where every constituent follows the negative binomial distribution with arbitrary parameters. We derive the exact probability mass function and the cumulative probability function of S. We also show that one can relate to the distribution of S as a mixture negative binomial distribution.
Author : Erik Bølviken
Publisher : Cambridge University Press
ISBN 13 : 1107782627
Total Pages : 713 pages
Book Rating : 4.1/5 (77 download)
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.
Author : Charalambos A. Charalambides
Publisher : John Wiley & Sons
ISBN 13 : 0471733172
Total Pages : 440 pages
Book Rating : 4.4/5 (717 download)
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.
