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Statistical Simulation

Author: Todd C. Headrick
Publisher: CRC Press
ISBN: 9781420064919
Size: 36.55 MB
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Although power method polynomials based on the standard normal distributions have been used in many different contexts for the past 30 years, it was not until recently that the probability density function (pdf) and cumulative distribution function (cdf) were derived and made available. Focusing on both univariate and multivariate nonnormal data generation, Statistical Simulation: Power Method Polynomials and Other Transformations presents techniques for conducting a Monte Carlo simulation study. It shows how to use power method polynomials for simulating univariate and multivariate nonnormal distributions with specified cumulants and correlation matrices. The book first explores the methodology underlying the power method, before demonstrating this method through examples of standard normal, logistic, and uniform power method pdfs. It also discusses methods for improving the performance of a simulation based on power method polynomials. The book then develops simulation procedures for systems of linear statistical models, intraclass correlation coefficients, and correlated continuous variates and ranks. Numerical examples and results from Monte Carlo simulations illustrate these procedures. The final chapter describes how the g-and-h and generalized lambda distribution (GLD) transformations are special applications of the more general multivariate nonnormal data generation approach. Throughout the text, the author employs Mathematica® in a range of procedures and offers the source code for download online. Written by a longtime researcher of the power method, this book explains how to simulate nonnormal distributions via easy-to-use power method polynomials. By using the methodology and techniques developed in the text, readers can evaluate different transformations in terms of comparing percentiles, measures of central tendency, goodness-of-fit tests, and more.

Monte Carlo Simulation Based Statistical Modeling

Author: Ding-Geng (Din) Chen
Publisher: Springer
ISBN: 9811033072
Size: 39.53 MB
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This book brings together expert researchers engaged in Monte-Carlo simulation-based statistical modeling, offering them a forum to present and discuss recent issues in methodological development as well as public health applications. It is divided into three parts, with the first providing an overview of Monte-Carlo techniques, the second focusing on missing data Monte-Carlo methods, and the third addressing Bayesian and general statistical modeling using Monte-Carlo simulations. The data and computer programs used here will also be made publicly available, allowing readers to replicate the model development and data analysis presented in each chapter, and to readily apply them in their own research. Featuring highly topical content, the book has the potential to impact model development and data analyses across a wide spectrum of fields, and to spark further research in this direction.

Simulating Data With Sas

Author: Rick Wicklin
Publisher: SAS Institute
ISBN: 1629592536
Size: 68.28 MB
Format: PDF, Kindle
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Data simulation is a fundamental technique in statistical programming and research. Rick Wicklin's Simulating Data with SAS brings together the most useful algorithms and the best programming techniques for efficient data simulation in an accessible how-to book for practicing statisticians and statistical programmers. This book discusses in detail how to simulate data from common univariate and multivariate distributions, and how to use simulation to evaluate statistical techniques. It also covers simulating correlated data, data for regression models, spatial data, and data with given moments. It provides tips and techniques for beginning programmers, and offers libraries of functions for advanced practitioners. As the first book devoted to simulating data across a range of statistical applications, Simulating Data with SAS is an essential tool for programmers, analysts, researchers, and students who use SAS software. This book is part of the SAS Press program.

Current Topics In The Theory And Application Of Latent Variable Models

Author: Michael C. Edwards
Publisher: Routledge
ISBN: 1136699791
Size: 80.91 MB
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This book presents recent developments in the theory and application of latent variable models (LVMs) by some of the most prominent researchers in the field. Topics covered involve a range of LVM frameworks including item response theory, structural equation modeling, factor analysis, and latent curve modeling, as well as various non-standard data structures and innovative applications. The book is divided into two sections, although several chapters cross these content boundaries. Part one focuses on complexities which involve the adaptation of latent variables models in research problems where real-world conditions do not match conventional assumptions. Chapters in this section cover issues such as analysis of dyadic data and complex survey data, as well as analysis of categorical variables. Part two of the book focuses on drawing real-world meaning from results obtained in LVMs. In this section there are chapters examining issues involving assessment of model fit, the nature of uncertainty in parameter estimates, inferences, and the nature of latent variables and individual differences. This book appeals to researchers and graduate students interested in the theory and application of latent variable models. As such, it serves as a supplementary reading in graduate level courses on latent variable models. Prerequisites include basic knowledge of latent variable models.

Einf Hrung In Statistik Und Messwertanalyse F R Physiker

Author: G. Bohm
ISBN: 9783540257592
Size: 46.43 MB
Format: PDF
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Die Einf]hrung in die Statistik und Messwertanalyse f]r Physiker richtet sich weniger an mathematischen \berlegungen aus, sondern stellt die praktische Anwendung in den Vordergrund und schdrft die Intuition experimentelle Ergebnisse richtig einzuschdtzen. Zahlreiche ausf]hrlich betrachtete Beispiele dienen dazu, hdufig bei der Datenanalyse gemachte Fehler zu vermeiden (unsinnige Anwendung des Chi-Quadrattests, Funktionenanpassung bei falscher Parametrisierung, Entfaltung mit willk]rlicher Regularisierung). Ein besonderes Augenmerk wird auf den Vergleich von Daten mit Monte-Carlo-Simulationen gelenkt. Moderne Experimente kommen nicht ohne Simulation aus. Deshalb ist es wichtig zu wissen, wie Parameteranpassungen und Entfaltungen in diesem Fall durchgef]rt werden. Au_erdem werden den Studierenden moderne Entwicklungen der Statistik nahegebracht, die in dlteren Lehrb]chern nicht behandelt werden.

Real Data Analysis

Author: Shlomo S. Sawilowsky
Publisher: Information Age Publishing
ISBN: 9781593115654
Size: 28.81 MB
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The invited authors of this edited volume have been prolific in the arena of Real Data Analysis (RDA) as it applies to the social and behavioral sciences, especially in the disciplines of education and psychology. Combined, this brain trust represents 3,247 articles in refereed journals, 127 books published, US $45.3 Million in extramural research funding, 34 teaching and 92 research awards, serve(d) as Editor/Assistant Editor/Editorial Board Member for 95 peer reviewed journals, and provide( d) ad hoc reviews for 362 journals. Their enormous footprint on real data analysis is showcased for professors, researchers, educators, administrators, and graduate students in the second text in the AERA/SIG ES Quantitative Methods series.

Simulating Univariate And Multivariate Nonnormal Distributions Based On A System Of Power Method Distributions

Author: Flaviu-Adrian Hodis
Size: 49.69 MB
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The purpose of this dissertation was to develop a system of power method non-normal distributions based on polynomial transformations of order three. A primary focus was to develop the methodology to provide users the ability to simulate univariate and multivariate non-normal distributions with specified standardized cumulants and arbitrary correlation matrices in a computationally efficient manner. The moment-matching methodology used to derive a particular family of power method distributions and its associated boundary condition in terms of skew and kurtosis is general provided the required moments exist. For example, a family of distributions could be based on a transformation of a normal, triangular, uniform, t , or logistic distribution. However, in view of this investigation, the system of distributions that appears most promising in the context of both univariate and multivariate data generation is a system based on standard (a) normal, (b) logistic, and (c) uniform distributions. The system of non-normal distributions studied in this investigation was demonstrated to have valid power method probability density functions (pdfs) and distribution functions. The specific boundary condition for each family of pdfs within this system was also provided. In view of this, it was demonstrated that the computation of probabilities, percentiles, and trimmed means could be done with relative ease. Numerical examples and graphs of power method pdfs are provided to confirm and illustrate the methodology. It was also shown how the power method could be applied in context of distribution fitting using real-world data. Monte Carlo results are provided to demonstrate that the power method accurately generates the specified cumulants and correlations both within and between the system's non-normal distributions.

Computer Intensive Und Nichtparametrische Statistische Tests

Author: Markus Neuhäuser
Publisher: Oldenbourg Verlag
ISBN: 9783486588859
Size: 48.15 MB
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Dieses Lehrbuch fuhrt verstandlich in nichtparametrische Tests ein; besondere Berucksichtigung finden Permutations- und Bootstrap-Tests, die seit der zweiten Halfte der 1990er mehr und mehr in den Vordergrund rucken und inzwischen in zahlreichen statistischen Programmsystemen implementiert wurden. Auf die Vorstellung der verschiedenen Testverfahren folgt die Bearbeitung konkreter, beispielhafter Testprobleme. Zudem werden Programme umfassend vorgestellt, so dass der Leser in der Lage ist, die Verfahren selbst anzuwenden."

Uncertainty Assessment Of Large Finite Element Systems

Author: Christian A. Schenk
Publisher: Springer Science & Business Media
ISBN: 9783540253433
Size: 78.63 MB
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The treatment of uncertainties in the analysis of engineering structures remains one of the premium challenges in modern structural mechanics. It is only in recent years that the developments in stochastic and deterministic computational mechanics began to be synchronized. To foster these developments, novel computational procedures for the uncertainty assessment of large finite element systems are presented in this monograph. The stochastic input is modeled by the so-called Karhunen-Loève expansion, which is formulated in this context both for scalar and vector stochastic processes as well as for random fields. Particularly for strongly non-linear structures and systems the direct Monte Carlo simulation technique has proven to be most advantageous as method of solution. The capabilities of the developed procedures are demonstrated by showing some practical applications.

Algorithmen Eine Einf Hrung

Author: Thomas H. Cormen
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110522012
Size: 78.71 MB
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Der "Cormen" bietet eine umfassende und vielseitige Einführung in das moderne Studium von Algorithmen. Es stellt viele Algorithmen Schritt für Schritt vor, behandelt sie detailliert und macht deren Entwurf und deren Analyse allen Leserschichten zugänglich. Sorgfältige Erklärungen zur notwendigen Mathematik helfen, die Analyse der Algorithmen zu verstehen. Den Autoren ist es dabei geglückt, Erklärungen elementar zu halten, ohne auf Tiefe oder mathematische Exaktheit zu verzichten. Jedes der weitgehend eigenständig gestalteten Kapitel stellt einen Algorithmus, eine Entwurfstechnik, ein Anwendungsgebiet oder ein verwandtes Thema vor. Algorithmen werden beschrieben und in Pseudocode entworfen, der für jeden lesbar sein sollte, der schon selbst ein wenig programmiert hat. Zahlreiche Abbildungen verdeutlichen, wie die Algorithmen arbeiten. Ebenfalls angesprochen werden Belange der Implementierung und andere technische Fragen, wobei, da Effizienz als Entwurfskriterium betont wird, die Ausführungen eine sorgfältige Analyse der Laufzeiten der Programme mit ein schließen. Über 1000 Übungen und Problemstellungen und ein umfangreiches Quellen- und Literaturverzeichnis komplettieren das Lehrbuch, dass durch das ganze Studium, aber auch noch danach als mathematisches Nachschlagewerk oder als technisches Handbuch nützlich ist. Für die dritte Auflage wurde das gesamte Buch aktualisiert. Die Änderungen sind vielfältig und umfassen insbesondere neue Kapitel, überarbeiteten Pseudocode, didaktische Verbesserungen und einen lebhafteren Schreibstil. So wurden etwa - neue Kapitel zu van-Emde-Boas-Bäume und mehrfädigen (engl.: multithreaded) Algorithmen aufgenommen, - das Kapitel zu Rekursionsgleichungen überarbeitet, sodass es nunmehr die Teile-und-Beherrsche-Methode besser abdeckt, - die Betrachtungen zu dynamischer Programmierung und Greedy-Algorithmen überarbeitet; Memoisation und der Begriff des Teilproblem-Graphen als eine Möglichkeit, die Laufzeit eines auf dynamischer Programmierung beruhender Algorithmus zu verstehen, werden eingeführt. - 100 neue Übungsaufgaben und 28 neue Problemstellungen ergänzt. Umfangreiches Dozentenmaterial (auf englisch) ist über die Website des US-Verlags verfügbar.