Automatic Nonuniform Random Variate Generation

Automatic Nonuniform Random Variate Generation
Author: Wolfgang Hörmann
Publisher: Springer Science & Business Media
Total Pages: 439
Release: 2013-06-29
Genre: Mathematics
ISBN: 3662059460

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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.

Automatic Nonuniform Random Variate Generation in R.

Automatic Nonuniform Random Variate Generation in R.
Author:
Publisher:
Total Pages:
Release: 2003
Genre:
ISBN:

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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).

Non-Uniform Random Variate Generation

Non-Uniform Random Variate Generation
Author: Luc Devroye
Publisher: Springer Science & Business Media
Total Pages: 859
Release: 2013-11-22
Genre: Mathematics
ISBN: 1461386438

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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."

Automatic Random Variate Generation for Simulation Input

Automatic Random Variate Generation for Simulation Input
Author:
Publisher:
Total Pages:
Release: 2000
Genre:
ISBN:

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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).

Proceedings of COMPSTAT'2010

Proceedings of COMPSTAT'2010
Author: Yves Lechevallier
Publisher: Springer Science & Business Media
Total Pages: 627
Release: 2010-11-08
Genre: Computers
ISBN: 3790826049

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Proceedings of the 19th international symposium on computational statistics, held in Paris august 22-27, 2010.Together with 3 keynote talks, there were 14 invited sessions and more than 100 peer-reviewed contributed communications.

A Guide to Simulation

A Guide to Simulation
Author: P. Bratley
Publisher: Springer Science & Business Media
Total Pages: 399
Release: 2012-12-06
Genre: Science
ISBN: 146840167X

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Simulation means driving a model of a system with suitable inputs and observing the corresponding outputs. It is widely applied in engineering, in business, and in the physical and social sciences. Simulation method ology araws on computer. science, statistics, and operations research and is now sufficiently developed and coherent to be called a discipline in its own right. A course in simulation is an essential part of any operations re search or computer science program. A large fraction of applied work in these fields involves simulation; the techniques of simulation, as tools, are as fundamental as those of linear programming or compiler construction, for example. Simulation sometimes appears deceptively easy, but perusal of this book will reveal unexpected depths. Many simulation studies are statistically defective and many simulation programs are inefficient. We hope that our book will help to remedy this situation. It is intended to teach how to simulate effectively. A simulation project has three crucial components, each of which must always be tackled: (1) data gathering, model building, and validation; (2) statistical design and estimation; (3) programming and implementation. Generation of random numbers (Chapters 5 and 6) pervades simulation, but unlike the three components above, random number generators need not be constructed from scratch for each project. Usually random number packages are available. That is one reason why the chapters on random numbers, which contain mainly reference material, follow the ch!lPters deal ing with experimental design and output analysis.

Advances in Modeling and Simulation

Advances in Modeling and Simulation
Author: Zdravko Botev
Publisher: Springer Nature
Total Pages: 426
Release: 2022-11-30
Genre: Mathematics
ISBN: 3031101936

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This book celebrates the career of Pierre L’Ecuyer on the occasion of his 70th birthday. Pierre has made significant contributions to the fields of simulation, modeling, and operations research over the last 40 years. This book contains 20 chapters written by collaborators and experts in the field who, by sharing their latest results, want to recognize the lasting impact of Pierre’s work in their research area. The breadth of the topics covered reflects the remarkable versatility of Pierre's contributions, from deep theoretical results to practical and industry-ready applications. The Festschrift features article from the domains of Monte Carlo and quasi-Monte Carlo methods, Markov chains, sampling and low discrepancy sequences, simulation, rare events, graphics, finance, machine learning, stochastic processes, and tractability.

Handbook of Computational Statistics

Handbook of Computational Statistics
Author: James E. Gentle
Publisher: Springer
Total Pages: 0
Release: 2017-05-04
Genre: Computers
ISBN: 9783662517659

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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.

Algorithms and Computation

Algorithms and Computation
Author: Leizhen Cai
Publisher: Springer
Total Pages: 761
Release: 2013-12-12
Genre: Computers
ISBN: 364245030X

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This book constitutes the refereed proceedings of the 24th International Symposium on Algorithms and Computation, ISAAC 2013, held in Hong Kong, China in December 2013. The 67 revised full papers presented together with 2 invited talks were carefully reviewed and selected from 177 submissions for inclusion in the book. The focus of the volume in on the following topics: computation geometry, pattern matching, computational complexity, internet and social network algorithms, graph theory and algorithms, scheduling algorithms, fixed-parameter tractable algorithms, algorithms and data structures, algorithmic game theory, approximation algorithms and network algorithms.

Independent Random Sampling Methods

Independent Random Sampling Methods
Author: Luca Martino
Publisher: Springer
Total Pages: 289
Release: 2018-03-31
Genre: Computers
ISBN: 331972634X

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This book systematically addresses the design and analysis of efficient techniques for independent random sampling. Both general-purpose approaches, which can be used to generate samples from arbitrary probability distributions, and tailored techniques, designed to efficiently address common real-world practical problems, are introduced and discussed in detail. In turn, the monograph presents fundamental results and methodologies in the field, elaborating and developing them into the latest techniques. The theory and methods are illustrated with a varied collection of examples, which are discussed in detail in the text and supplemented with ready-to-run computer code. The main problem addressed in the book is how to generate independent random samples from an arbitrary probability distribution with the weakest possible constraints or assumptions in a form suitable for practical implementation. The authors review the fundamental results and methods in the field, address the latest methods, and emphasize the links and interplay between ostensibly diverse techniques.