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Author: Wallace Robert Blischke
Publisher:
ISBN:
Category : Distribution (Probability theory)
Languages : en
Pages : 160
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Book Description
Two aspects to the problem of estimation in dealing with mixtures of distributions are considered. The first is the question of identifiability. A distribution function F which is a probability mixture of distribution functions belonging to some family D is identifiable if F can be written in only one way as a probability mixture of elements of D. The second aspect of the estimation problem is concerned with the construction for identifiable mixtures of estimators of the parameters of the component distributions and of the mixing measure. These problems are considered for mixtures of a known finite number. (Author).
Author: Wallace Robert Blischke
Publisher:
ISBN:
Category : Distribution (Probability theory)
Languages : en
Pages : 160
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Book Description
Two aspects to the problem of estimation in dealing with mixtures of distributions are considered. The first is the question of identifiability. A distribution function F which is a probability mixture of distribution functions belonging to some family D is identifiable if F can be written in only one way as a probability mixture of elements of D. The second aspect of the estimation problem is concerned with the construction for identifiable mixtures of estimators of the parameters of the component distributions and of the mixing measure. These problems are considered for mixtures of a known finite number. (Author).
Author: B. Everitt
Publisher: Springer Science & Business Media
ISBN: 9400958978
Category : Science
Languages : en
Pages : 148
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Book Description
Finite mixture distributions arise in a variety of applications ranging from the length distribution of fish to the content of DNA in the nuclei of liver cells. The literature surrounding them is large and goes back to the end of the last century when Karl Pearson published his well-known paper on estimating the five parameters in a mixture of two normal distributions. In this text we attempt to review this literature and in addition indicate the practical details of fitting such distributions to sample data. Our hope is that the monograph will be useful to statisticians interested in mixture distributions and to re search workers in other areas applying such distributions to their data. We would like to express our gratitude to Mrs Bertha Lakey for typing the manuscript. Institute oj Psychiatry B. S. Everitt University of London D. l Hand 1980 CHAPTER I General introduction 1. 1 Introduction This monograph is concerned with statistical distributions which can be expressed as superpositions of (usually simpler) component distributions. Such superpositions are termed mixture distributions or compound distributions. For example, the distribution of height in a population of children might be expressed as follows: h(height) = fg(height: age)f(age)d age (1. 1) where g(height: age) is the conditional distribution of height on age, and/(age) is the age distribution of the children in the population.
Author:
Publisher:
ISBN:
Category : Weights and measures
Languages : en
Pages : 574
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Book Description
Author: Matthew S. Wood
Publisher:
ISBN:
Category :
Languages : en
Pages : 286
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Author: Norman L. Johnson
Publisher: John Wiley & Sons
ISBN: 0471715808
Category : Mathematics
Languages : en
Pages : 676
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Book Description
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: Charalambos A. Charalambides
Publisher: John Wiley & Sons
ISBN: 0471733172
Category : Mathematics
Languages : en
Pages : 440
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Book Description
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.
Author: A. Clifford Cohen
Publisher:
ISBN:
Category : Distribution (Probability theory)
Languages : en
Pages : 100
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Book Description
Author: Brian L. Joiner
Publisher:
ISBN:
Category : Annals of mathematical statistics
Languages : en
Pages : 512
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Book Description
All articles, notes, queries, corrigenda, and obituaries appearing in the following journals during the indicated years are indexed: Annals of mathematical statistics, 1961-1969; Biometrics, 1965-1969#3; Biometrics, 1951-1969; Journal of the American Statistical Association, 1956-1969; Journal of the Royal Statistical Society, Series B, 1954-1969,#2; South African statistical journal, 1967-1969,#2; Technometrics, 1959-1969.--p.iv.
Author: Anirban DasGupta
Publisher: Springer Science & Business Media
ISBN: 0387759719
Category : Mathematics
Languages : en
Pages : 727
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Book Description
This unique book delivers an encyclopedic treatment of classic as well as contemporary large sample theory, dealing with both statistical problems and probabilistic issues and tools. The book is unique in its detailed coverage of fundamental topics. It is written in an extremely lucid style, with an emphasis on the conceptual discussion of the importance of a problem and the impact and relevance of the theorems. There is no other book in large sample theory that matches this book in coverage, exercises and examples, bibliography, and lucid conceptual discussion of issues and theorems.
Author: Defense Documentation Center (U.S.)
Publisher:
ISBN:
Category : Military art and science
Languages : en
Pages : 1540
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Book Description
