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Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
We develop and evaluate algorithms for generating random variates for simulation input. One group called automatic, or black-box algorithms can be used to sample from distributions with known density. They are based on the rejection principle. The hat function is generated automatically in a setup step using the idea of transformed density rejection. There the density is transformed into a concave function and the minimum of several tangents is used to construct the hat function. The resulting algorithms are not too complicated and are quite fast. The principle is also applicable to random vectors. A second group of algorithms is presented that generate random variates directly from a given sample by implicitly estimating the unknown distribution. The best of these algorithms are based on the idea of naive resampling plus added noise. These algorithms can be interpreted as sampling from the kernel density estimates. This method can be also applied to random vectors. There it can be interpreted as a mixture of naive resampling and sampling from the multi-normal distribution that has the same covariance matrix as the data. The algorithms described in this paper have been implemented in ANSI C in a library called UNURAN which is available via anonymous ftp. (author's abstract).
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
We develop and evaluate algorithms for generating random variates for simulation input. One group called automatic, or black-box algorithms can be used to sample from distributions with known density. They are based on the rejection principle. The hat function is generated automatically in a setup step using the idea of transformed density rejection. There the density is transformed into a concave function and the minimum of several tangents is used to construct the hat function. The resulting algorithms are not too complicated and are quite fast. The principle is also applicable to random vectors. A second group of algorithms is presented that generate random variates directly from a given sample by implicitly estimating the unknown distribution. The best of these algorithms are based on the idea of naive resampling plus added noise. These algorithms can be interpreted as sampling from the kernel density estimates. This method can be also applied to random vectors. There it can be interpreted as a mixture of naive resampling and sampling from the multi-normal distribution that has the same covariance matrix as the data. The algorithms described in this paper have been implemented in ANSI C in a library called UNURAN which is available via anonymous ftp. (author's abstract).
Author: Wolfgang Hörmann
Publisher: Springer Science & Business Media
ISBN: 3662059460
Category : Mathematics
Languages : en
Pages : 439
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Book Description
The recent concept of universal (also called automatic or black-box) random variate generation can only be found dispersed in the literature. Being unique in its overall organization, the book covers not only the mathematical and statistical theory but also deals with the implementation of such methods. All algorithms introduced in the book are designed for practical use in simulation and have been coded and made available by the authors. Examples of possible applications of the presented algorithms (including option pricing, VaR and Bayesian statistics) are presented at the end of the book.
Author: Wolfgang Hörmann
Publisher: Springer
ISBN: 9783642073724
Category : Mathematics
Languages : en
Pages : 0
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Book Description
The recent concept of universal (also called automatic or black-box) random variate generation can only be found dispersed in the literature. Being unique in its overall organization, the book covers not only the mathematical and statistical theory but also deals with the implementation of such methods. All algorithms introduced in the book are designed for practical use in simulation and have been coded and made available by the authors. Examples of possible applications of the presented algorithms (including option pricing, VaR and Bayesian statistics) are presented at the end of the book.
Author: James E. Gentle
Publisher: Springer Science & Business Media
ISBN: 3642215513
Category : Computers
Languages : en
Pages : 1180
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Book Description
The Handbook of Computational Statistics - Concepts and Methods (second edition) is a revision of the first edition published in 2004, and contains additional comments and updated information on the existing chapters, as well as three new chapters addressing recent work in the field of computational statistics. This new edition is divided into 4 parts in the same way as the first edition. It begins with "How Computational Statistics became the backbone of modern data science" (Ch.1): an overview of the field of Computational Statistics, how it emerged as a separate discipline, and how its own development mirrored that of hardware and software, including a discussion of current active research. The second part (Chs. 2 - 15) presents several topics in the supporting field of statistical computing. Emphasis is placed on the need for fast and accurate numerical algorithms, and some of the basic methodologies for transformation, database handling, high-dimensional data and graphics treatment are discussed. The third part (Chs. 16 - 33) focuses on statistical methodology. Special attention is given to smoothing, iterative procedures, simulation and visualization of multivariate data. Lastly, a set of selected applications (Chs. 34 - 38) like Bioinformatics, Medical Imaging, Finance, Econometrics and Network Intrusion Detection highlight the usefulness of computational statistics in real-world applications.
Author: Yuichi Mori
Publisher: Springer Science & Business Media
ISBN: 9783540404644
Category : Computers
Languages : en
Pages : 1096
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Book Description
The Handbook of Computational Statistics: Concepts and Methodology is divided into four parts. It begins with an overview over the field of Computational Statistics. The second part presents several topics in the supporting field of statistical computing. Emphasis is placed on the need of fast and accurate numerical algorithms and it discusses some of the basic methodologies for transformation, data base handling and graphics treatment. The third part focuses on statistical methodology. Special attention is given to smoothing, iterative procedures, simulation and visualization of multivariate data. Finally a set of selected applications like Bioinformatics, Medical Imaging, Finance and Network Intrusion Detection highlight the usefulness of computational statistics.
Author: John Dagpunar
Publisher: Oxford University Press, USA
ISBN:
Category : Language Arts & Disciplines
Languages : en
Pages : 256
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Book Description
An up-to-date account of the theory and practice of generating random variates from probability distributions is presented in this accessible text. After a brief introduction to simulation, the author discusses the general principles for generating and testing uniform and non-uniform variates. These techniques are applied to univariate and multivariate distributions, Markov processes, and order statistics. Dr. Dagpunar has included Fortran 77 programs for generating the more familiar distributions and a set of graphical aids for the manual generation of variates. Competing methods are also compared and their advantages and disadvantages discussed. In addition, algorithms throughout the book enable readers to generate variates from selected distributions, making this an invaluable guide for statisticians, operational researchers, computer scientists, and postgraduates engaged in computer simulation.
Author: Luc Devroye
Publisher: Springer Science & Business Media
ISBN: 1461386438
Category : Mathematics
Languages : en
Pages : 859
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Book Description
Thls text ls about one small fteld on the crossroads of statlstlcs, operatlons research and computer sclence. Statistleians need random number generators to test and compare estlmators before uslng them ln real l fe. In operatlons research, random numbers are a key component ln arge scale slmulatlons. Computer sclen tlsts need randomness ln program testlng, game playlng and comparlsons of algo rlthms. The appl catlons are wlde and varled. Yet all depend upon the same com puter generated random numbers. Usually, the randomness demanded by an appl catlon has some bullt-ln structure: typlcally, one needs more than just a sequence of Independent random blts or Independent uniform 0,1] random vari ables. Some users need random variables wlth unusual densltles, or random com blnatorlal objects wlth speclftc propertles, or random geometrlc objects, or ran dom processes wlth weil deftned dependence structures. Thls ls preclsely the sub ject area of the book, the study of non-uniform random varlates. The plot evolves around the expected complexlty of random varlate genera tlon algorlthms. We set up an ldeal zed computatlonal model (wlthout overdolng lt), we lntroduce the notlon of unlformly bounded expected complexlty, and we study upper and lower bounds for computatlonal complexlty. In short, a touch of computer sclence ls added to the fteld. To keep everythlng abstract, no tlmlngs or computer programs are lncluded. Thls was a Iabor of Iove. George Marsagl a created CS690, a course on ran dom number generat on at the School of Computer Sclence of McG ll Unlverslty."
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Random variate genration is an important tool in statistical computing. Many programms for simulation or statistical computing (e.g. R) provide a collection of random variate generators for many standard distributions. However, as statistical modeling has become more sophisticated there is demand for larger classes of distributions. Adding generators for newly required distribution seems not to be the solution to this problem. Instead so called automatic (or black-box) methods have been developed in the last decade for sampling from fairly large classes of distributions with a single piece of code. For such algorithms a data about the distributions must be given; typically the density function (or probability mass function), and (maybe) the (approximate) location of the mode. In this contribution we show how such algorithms work and suggest an interface for R as an example of a statistical library. (author's abstract).
Author: B. W. Schmeiser
Publisher:
ISBN:
Category : Distribution (Probability theory)
Languages : en
Pages : 12
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Book Description
The research topic was the probabilistic and statistical issues associated with simulating stochastic systems on digital computers. Throughout the duration of the project, results were obtained in the areas of input modeling and random variate generation, as indicated by the project title. During the last two years, results were also obtained in output analysis and variance reduction. Areas researched include: Input modeling the selection, fitting, and checking of probabilistic models of exogenous simulation variables used to drive simulation models; Random variate generation; Output analysis - the treatment of the data generated by the simulation model; and; Variance reduction - the transformation from on simulation experiment to another for the purpose of obtaining better properties for the Monte Carlo estimator(s).
Author: Michael W. Carter
Publisher: CRC Press
ISBN: 9780849322563
Category : Technology & Engineering
Languages : en
Pages : 414
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Book Description
Students with diverse backgrounds will face a multitude of decisions in a variety of engineering, scientific, industrial, and financial settings. They will need to know how to identify problems that the methods of operations research (OR) can solve, how to structure the problems into standard mathematical models, and finally how to apply or develop computational tools to solve the problems. Perfect for any one-semester course in OR, Operations Research: A Practical Introduction answers all of these needs. In addition to providing a practical introduction and guide to using OR techniques, it includes a timely examination of innovative methods and practical issues related to the development and use of computer implementations. It provides a sound introduction to the mathematical models relevant to OR and illustrates the effective use of OR techniques with examples drawn from industrial, computing, engineering, and business applications Many students will take only one course in the techniques of Operations Research. Operations Research: A Practical Introduction offers them the greatest benefit from that course through a broad survey of the techniques and tools available for quantitative decision making. It will also encourage other students to pursue more advanced studies and provides you a concise, well-structured, vehicle for delivering the best possible overview of the discipline.
