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Author: J Grandell
Publisher: CRC Press
ISBN: 1000109992
Category : Mathematics
Languages : en
Pages : 281
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Book Description
To date, Mixed Poisson processes have been studied by scientists primarily interested in either insurance mathematics or point processes. Work in one area has often been carried out without knowledge of the other area. Mixed Poisson Processes is the first book to combine and concentrate on these two themes, and to distinguish between the notions of distributions and processes. The first part of the text gives special emphasis to the estimation of the underlying intensity, thinning, infinite divisibility, and reliability properties. The second part is, to a greater extent, based on Lundberg's thesis.
Author: Varahamurti Raghavendra Krishna
Publisher:
ISBN:
Category : Poisson distribution
Languages : en
Pages : 0
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Book Description
Abstract. A considerable volume of recent research work has been devoted to mixtures of discrete distributions. The purpose of this thesis is to obtain estimates of the parameters of the mixed-Poisson distribution and also to study their mathematical properties. In Chapter 1, some recent work in these fields is reviewed, namely the work of Gumbel [15], Rider [26] and Blischke [4]. Chapter II, contains a detailed discussion of the derivation of the mixed Poisson distribution. In Chapter III, moment estimators for a mixture of two Poisson distributions are obtained and their asymptotic properties discussed. Chapter IV, contains a variety of results which are obtained as a by product of our approach.
Author: J Grandell
Publisher: CRC Press
ISBN: 1000109992
Category : Mathematics
Languages : en
Pages : 281
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Book Description
To date, Mixed Poisson processes have been studied by scientists primarily interested in either insurance mathematics or point processes. Work in one area has often been carried out without knowledge of the other area. Mixed Poisson Processes is the first book to combine and concentrate on these two themes, and to distinguish between the notions of distributions and processes. The first part of the text gives special emphasis to the estimation of the underlying intensity, thinning, infinite divisibility, and reliability properties. The second part is, to a greater extent, based on Lundberg's thesis.
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: Frank A. Haight
Publisher:
ISBN:
Category : Poisson distribution
Languages : en
Pages : 192
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Book Description
Author: Kathryn Jo-Anne Barger
Publisher:
ISBN:
Category :
Languages : en
Pages : 228
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Author: A. Clifford Cohen
Publisher:
ISBN:
Category : Distribution (Probability theory)
Languages : en
Pages : 18
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Book Description
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: Mina Habibi
Publisher:
ISBN:
Category : Multiscalemodeling
Languages : en
Pages : 13
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Book Description
In this article, a new mixed Poisson distribution that includes the geometric and negative binomial distributions as special cases is proposed. This distribution is obtained by mixing the Poisson distribution with the binomial exponential 2 distribution. The new distribution is overdispersed (i.e., the variance is greater than the mean), and hence, this distribution is able to incorporate the overdispersion that typically occurs in count data sets. Shape and moments properties of the proposed distribution are discussed. Estimation of the model parameters is considered using the method of moments and maximum likelihood approach. We propose an algorithm for generating random data from the new distribution. Three real data applications are also presented to see that new distribution is useful for modeling count data.
Author: Günter Last
Publisher: Cambridge University Press
ISBN: 1107088011
Category : Mathematics
Languages : en
Pages : 315
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Book Description
A modern introduction to the Poisson process, with general point processes and random measures, and applications to stochastic geometry.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
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