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Author :
Publisher : Springer-Verlag
ISBN 13 : 3663091961
Total Pages : 211 pages
Book Rating : 4.67/5 ( download)
Download or read book A Concept of Generalized Order Statistics written by and published by Springer-Verlag. This book was released on 2013-07-01 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Erhard Cramer
Publisher :
ISBN 13 :
Total Pages : 169 pages
Book Rating : 4.72/5 ( download)
Download or read book Contributions to Generalized Order Statistics written by Erhard Cramer and published by . This book was released on 2003 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Udo Kamps
Publisher : Teubner Skripten zur Mathematischen Stochastik
ISBN 13 :
Total Pages : 220 pages
Book Rating : 4.62/5 ( download)
Download or read book A Concept of Generalized Order Statistics written by Udo Kamps and published by Teubner Skripten zur Mathematischen Stochastik. This book was released on 1995 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Order statistics and record values appear in many statistical applications and are widely used in statistical modeling and inference. Both models describe random variables arranged in order of magnitude. In addition to these well-known models, several other models of ordered random variables, known and new ones, are introduced in this book such as order statistics with non-integral sample size, sequential order statistics, k-th record values, Pfeifer' s record model, k -records from non-identical distributions and ordered random variables which arise from n truncation of distributions. These models can be effectively applied, e.g., in reliability theory. Here, an order statistic represents the life-length of some r-out-of-n-system which is an important technical structure consisting of n components. For this application, a new and more adequate model is naturally suggested. Sequential order statistics serve as a model describing certain dependencies or interactions among the system components caused by failures of components. Record values are closely connected with the occurrence times of some corresponding non-homogeneaus Poisson process and used in so lled shock models. More flexible record models, and therefore more applicable to practical situations, are considered here. The main purpose of this book is to present a concept of generalized order statistics as a unified approach to a variety of models of ordered random variables. In the distribution theoretical sense, all of the models mentioned above are contained in the proposed model of generalized order statistics.
Author : Barry C. Arnold
Publisher : SIAM
ISBN 13 : 0898716489
Total Pages : 291 pages
Book Rating : 4.81/5 ( download)
Download or read book A First Course in Order Statistics written by Barry C. Arnold and published by SIAM. This book was released on 2008-09-25 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This updated classic text will aid readers in understanding much of the current literature on order statistics: a flourishing field of study that is essential for any practising statistician and a vital part of the training for students in statistics. Written in a simple style that requires no advanced mathematical or statistical background, the book introduces the general theory of order statistics and their applications. The book covers topics such as distribution theory for order statistics from continuous and discrete populations, moment relations, bounds and approximations, order statistics in statistical inference and characterisation results, and basic asymptotic theory. There is also a short introduction to record values and related statistics. The authors have updated the text with suggestions for further reading that may be used for self-study. Written for advanced undergraduate and graduate students in statistics and mathematics, practising statisticians, engineers, climatologists, economists, and biologists.
Author : Narayanaswamy Balakrishnan
Publisher : Elsevier
ISBN 13 : 1483297497
Total Pages : 399 pages
Book Rating : 4.91/5 ( download)
Download or read book Order Statistics & Inference written by Narayanaswamy Balakrishnan and published by Elsevier. This book was released on 2014-06-28 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: The literature on order statistics and inferenc eis quite extensive and covers a large number of fields ,but most of it is dispersed throughout numerous publications. This volume is the consolidtion of the most important results and places an emphasis on estimation. Both theoretical and computational procedures are presented to meet the needs of researchers, professionals, and students. The methods of estimation discussed are well-illustrated with numerous practical examples from both the physical and life sciences, including sociology,psychology,a nd electrical and chemical engineering. A complete, comprehensive bibliography is included so the book can be used both aas a text and reference.
Author : Birgit Debrabant
Publisher : Logos Verlag Berlin GmbH
ISBN 13 : 3832519599
Total Pages : 154 pages
Book Rating : 4.99/5 ( download)
Download or read book Point Processes with a Generalized Order Statistic Property written by Birgit Debrabant and published by Logos Verlag Berlin GmbH. This book was released on 2008 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mixed Poisson processes are a well known class of point processes derived from (stationary) Poisson processes. In particular they cover cases where the intensity of a Poisson process is unknown but can be assumed to follow a known probability distribution. This situation is common e. g. in insurance mathematics where for instance the number of accident claims in which an individual is involved and which is evolving over some time can in principal be well described by a Poisson process with an individual, yet normally unknown intensity corresponding to the individual's accident proneness. Modelling this intensity as a random variable naturally leads to a mixed model. Usually, an insurance company will have a good estimate of the associated mixing distribution due to its large portfolio of policies.
Author : M. A. Abd Elgawad
Publisher : LAP Lambert Academic Publishing
ISBN 13 : 9783659631467
Total Pages : 128 pages
Book Rating : 4.69/5 ( download)
Download or read book Bivariate Generalized Order Statistics written by M. A. Abd Elgawad and published by LAP Lambert Academic Publishing. This book was released on 2014-10-31 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Kamps (1995) generalized order statistics (GOS) have been introduced as a unifying theme for several models of ascendingly ordered random variables (rv's). Following Kamps, Burkschat et al. (2003) have introduced the concept of dual generalized order statistics (DGOS) to unify several models that produce ordered rv's. The main aim of this book is to study the limit joint distribution function (df) of any two statistics in a wide subclass of the GOS and DGOS models known as m-GOS and m-DGOS respectively. This subclass contains many important practical models such as ordinary order statistics, order statistics with non-integer sample size, sequential order statistics and upper and lower record values. The limit df's of lower-lower extreme, upper-upper extreme, lower-upper extreme, central-central and lower-lower intermediate m-GOS and m-DGOS are obtained. It is revealed that the convergence of the marginals m-GOS and m-DGOS implies the convergence of the joint df. Moreover, the conditions, under which the asymptotic independence between the two marginals occurs, are derived.
Author : A. M. ELsawah
Publisher : LAP Lambert Academic Publishing
ISBN 13 : 9783659286063
Total Pages : 120 pages
Book Rating : 4.60/5 ( download)
Download or read book Generalized Order Statistics Under Finite Mixture Models written by A. M. ELsawah and published by LAP Lambert Academic Publishing. This book was released on 2014-03 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite mixture models have provided a mathematical-based approach in statistical modeling in a wide variety of random phenomena. FMM have been applied in astronomy, biology, genetic, medicine, psychiatry, economics, engineering and marketing, among many other fields in the biological, physical and social science. Kamps suggested a new theoretical approach, which is called generalized order statistics (GOS). This new model includes ordinary order statistics, sequential order statistics, progressive order statistics and record value. The main purpose of this book is to investigate the asymptotic behavior of the ordinary order statistics, generalized order statistics and dual generalized order statistics based on a random sample drawn from a finite mixture population with k components under general normalization. I obtain a sufficient conditions for this weak convergence, as well as the limit forms. Sufficient conditions are given to guarantee the existence of the weak convergence to non-degenerate distribution when the components are normalized by different normalization constants (linear-nonlinear). Illustrative examples of the most practically important distributions are obtained.
Author : HASAN MATEEN-UL ISLAM
Publisher : LAP Lambert Academic Publishing
ISBN 13 : 9783843379434
Total Pages : 140 pages
Book Rating : 4.32/5 ( download)
Download or read book Order Statistics, Records and Generalized Order Statistics written by HASAN MATEEN-UL ISLAM and published by LAP Lambert Academic Publishing. This book was released on 2010-12 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: In applied statistics, one observes a random quantity X, a number of times and based on these observations, one would like to conclude facts about the distribution function F(x) of X. The only method of finding distribution function F(x) exactly, which avoids the subjective choice, is a characterization theorem. Important consequence of characterization theorem is that these results help us in better understanding the structures and implications of the choice of distribution for a special problem. Regarding moments of generalized order statistics (gos), a concept introduced by Kamps (1995). Order and record statistics are particular cases of gos. Recurrence relations have great importance due to these reasons: (i). Reduce the amount of direct computations and hence reduce the time and labour (ii). They express the higher order moments in terms of the lower order moments and hence make the evaluation of higher order moments easy (iii). Provide simple checks to test the accuracy of computation of moments of order statistics. This book provides some new characterization and moments of order statistics, records and gos.
Author : Haroon Barakat
Publisher : LAP Lambert Academic Publishing
ISBN 13 : 9783659303449
Total Pages : 120 pages
Book Rating : 4.45/5 ( download)
Download or read book On the Asymptotic Generalized Order Statistics and Related Functions written by Haroon Barakat and published by LAP Lambert Academic Publishing. This book was released on 2012 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kamps (1995) suggested a new theoretical approach, which is called generalized order statistics (gos). This new model includes ordinary order statistics (oos), sequential order statistics, progressive type II censored order statistics and record values. The concept of gos enables a common approach to structural similarities and analogies. The distributional and inferential properties of oos and record values turn out to remain valid for gos (cf. Cramer and Kamps, 2001). Thus, the concept of gos provides a large class of models with many interesting and useful properties for both the description and the analysis of practical problems. Due to this reason, the question arises whether the general distribution theory of gos as well as their properties can be obtained by analogy with that for oos. The latter has been extensively investigated in the literature, e.g., see, David, 1981. The main purpose of this thesis is to investigate the asymptotic behavior of some important functions of gos, in view of theory of statistics and its applications. Some of these functions are non-linear, e.g., extremal product and extremal quotient and other are linear e.g., range and midrange.
