Normal and Student s t Distributions and Their Applications

Normal and Student   s t Distributions and Their Applications

The most important properties of normal and Student t-distributions are presented.

Author: Mohammad Ahsanullah

Publisher: Springer Science & Business Media

ISBN: 9789462390614

Category: Mathematics

Page: 157

View: 716

The most important properties of normal and Student t-distributions are presented. A number of applications of these properties are demonstrated. New related results dealing with the distributions of the sum, product and ratio of the independent normal and Student distributions are presented. The materials will be useful to the advanced undergraduate and graduate students and practitioners in the various fields of science and engineering.
Categories: Mathematics

Chance and Stability

Chance and Stability

The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.

Author: Vladimir V. Uchaikin

Publisher: Walter de Gruyter

ISBN: 9783110935974

Category: Mathematics

Page: 598

View: 356

The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.
Categories: Mathematics

Skew Elliptical Distributions and Their Applications

Skew Elliptical Distributions and Their Applications

A Journey Beyond Normality Marc G. Genton. Table 10.2 Distribution of firm size − difference in log marginal likelihood between the FS-t model and all ...

Author: Marc G. Genton

Publisher: CRC Press

ISBN: 9781135437312

Category: Mathematics

Page: 416

View: 977

This book reviews the state-of-the-art advances in skew-elliptical distributions and provides many new developments in a single volume, collecting theoretical results and applications previously scattered throughout the literature. The main goal of this research area is to develop flexible parametric classes of distributions beyond the classical normal distribution. The book is divided into two parts. The first part discusses theory and inference for skew-elliptical distribution. The second part examines applications and case studies, including areas such as economics, finance, oceanography, climatology, environmetrics, engineering, image processing, astronomy, and biomedical science.
Categories: Mathematics

Introduction to Biostatistical Applications in Health Research with Microsoft Office Excel and R

Introduction to Biostatistical Applications in Health Research with Microsoft Office Excel and R

Table B.2 presents values from Student's t-distribution and their ... of the table presenting values from the standard normal distribution (Table B.1).

Author: Robert P. Hirsch

Publisher: John Wiley & Sons

ISBN: 9781119722595

Category: Medical

Page: 640

View: 873

The second edition of Introduction to Biostatistical Applications in Health Research delivers a thorough examination of the basic techniques and most commonly used statistical methods in health research. Retaining much of what was popular with the well-received first edition, the thoroughly revised second edition includes a new chapter on testing assumptions and how to evaluate whether those assumptions are satisfied and what to do if they are not. The newest edition contains brand-new code examples for using the popular computer language R to perform the statistical analyses described in the chapters within. You’ll learn how to use Excel to generate datasets for R, which can then be used to conduct statistical calculations on your data. The book also includes a companion website with a new version of BAHR add-in programs for Excel. This new version contains new programs for nonparametric analyses, Student-Newman-Keuls tests, and stratified analyses. Readers will also benefit from coverage of topics like: Extensive discussions of basic and foundational concepts in statistical methods, including Bayes’ Theorem, populations, and samples A treatment of univariable analysis, covering topics like continuous dependent variables and ordinal dependent variables An examination of bivariable analysis, including regression analysis and correlation analysis An analysis of multivariate calculations in statistics and how testing assumptions, like assuming Gaussian distributions or equal variances, affect statistical outcomes Perfect for health researchers of all kinds, Introduction to Biostatistical Applications in Health Research also belongs on the bookshelves of anyone who wishes to better understand health research literature. Even those without a great deal of mathematical background will benefit greatly from this text.
Categories: Medical

Generalized Hyperbolic Secant Distributions

Generalized Hyperbolic Secant Distributions

​Among the symmetrical distributions with an infinite domain, the most popular alternative to the normal variant is the logistic distribution as well as the Laplace or the double exponential distribution, which was first introduced in ...

Author: Matthias J. Fischer

Publisher: Springer Science & Business Media

ISBN: 9783642451386

Category: Mathematics

Page: 72

View: 637

​Among the symmetrical distributions with an infinite domain, the most popular alternative to the normal variant is the logistic distribution as well as the Laplace or the double exponential distribution, which was first introduced in 1774. Occasionally, the Cauchy distribution is also used. Surprisingly, the hyperbolic secant distribution has led a charmed life, although Manoukian and Nadeau had already stated in 1988 that “... the hyperbolic-secant distribution ... has not received sufficient attention in the published literature and may be useful for students and practitioners.” During the last few years, however, several generalizations of the hyperbolic secant distribution have become popular in the context of financial return data because of its excellent fit. Nearly all of them are summarized within this Springer Brief.
Categories: Mathematics

Unbiased Estimators and their Applications

Unbiased Estimators and their Applications

This volume is a continuation of Unbiased Estimators and Their Applications, Vol.

Author: V.G. Voinov

Publisher: Springer Science & Business Media

ISBN: 0792339398

Category: Mathematics

Page: 262

View: 800

This volume is a continuation of Unbiased Estimators and Their Applications, Vol. I: Univariate Case. It contains problems of parametric point estimation for multivariate probability distributions emphasizing problems of unbiased estimation. The volume consists of four chapters dealing, respectively, with some basic properties of multivariate continuous and discrete distributions, the general theory of point estimation in multivariate case, techniques for constructing unbiased estimators and applications of unbiased estimation theory in the multivariate case. These chapters contain numerous examples, many applications and are followed by a comprehensive Appendix which classifies and lists, in the form of tables, all known results relating to unbiased estimators of parameter functions for multivariate distributions. Audience: This volume will serve as a handbook on point unbiased estimation for researchers whose work involves statistics. It can also be recommended as a supplementary text for undergraduate and graduate students.
Categories: Mathematics

Probability and Statistics Applications for Environmental Science

Probability and Statistics Applications for Environmental Science

The book's coverage is thorough, its presentation logical and geared to student's needs. It includes problems and solutions within the text and tables, a glossary of terms, and an introduction to design of experiments in the appendices.

Author: Stacey J Shaefer

Publisher: CRC Press

ISBN: 9780849375613

Category: Mathematics

Page: 367

View: 660

Simple, clear, and to the point, Probability and Statistics Applications for Environmental Science delineates the fundamentals of statistics, imparting a basic understanding of the theory and mechanics of the calculations. User-friendliness, uncomplicated explanations, and coverage of example applications in the environmental field set this book apart from other textbooks on the same subject. Striking a balance between theory and applied mathematics, the material is divided into three parts. Part I sets the stage with coverage of principles and fundamentals, such as set notation, probability distributions, and the estimation of the mean and variance. Part II discusses traditional statistics applications, centering around the uses of probability distributions, including how they relate to reliability and failure theory. The authors elucidate many of the important distributions, Monte Carlo methods, and fault and event trees. Part III delves into what some have come to define as contemporary statistics. It covers hypothesis testing, Student's t and chi-square tests, regression analysis, analysis of variance (ANOVA), and nonparametric tests. The book's coverage is thorough, its presentation logical and geared to student's needs. It includes problems and solutions within the text and tables, a glossary of terms, and an introduction to design of experiments in the appendices. The authors, known for their meticulously accurate, articulate, and practical writing style, master the difficult task of explaining very complicated subject matter in a way that is easily understood. The book features a clear, concise presentation that makes both teaching and learning easier.
Categories: Mathematics

Statistical Applications for Environmental Analysis and Risk Assessment

Statistical Applications for Environmental Analysis and Risk Assessment

The logarithm of the Pearson Type III distribution (i.e., Log-Pearson III)isan extreme value distribution often used to perform ... (Student'st,ChiSquare,.

Author: Joseph Ofungwu

Publisher: John Wiley & Sons

ISBN: 9781118634516

Category: Social Science

Page: 648

View: 737

Statistical Applications for Environmental Analysis and RiskAssessment guides readers through real-world situations and thebest statistical methods used to determine the nature and extent ofthe problem, evaluate the potential human health and ecologicalrisks, and design and implement remedial systems as necessary.Featuring numerous worked examples using actual data and“ready-made” software scripts, StatisticalApplications for Environmental Analysis and Risk Assessmentalso includes: • Descriptions of basic statistical concepts andprinciples in an informal style that does not presume priorfamiliarity with the subject • Detailed illustrations of statistical applications inthe environmental and related water resources fields usingreal-world data in the contexts that would typically be encounteredby practitioners • Software scripts using the high-powered statisticalsoftware system, R, and supplemented by USEPA’s ProUCL andUSDOE’s VSP software packages, which are all freelyavailable • Coverage of frequent data sample issues such asnon-detects, outliers, skewness, sustained and cyclical trend thathabitually plague environmental data samples • Clear demonstrations of the crucial, but oftenoverlooked, role of statistics in environmental sampling design andsubsequent exposure risk assessment.
Categories: Social Science

Statistics for Business

Statistics for Business

These three curves have a profile similar to the normal distribution but if we superimposed a normal distribution on a Student«s t distribution as shown in ...

Author: Derek L. Waller

Publisher: Routledge

ISBN: 9781134505005

Category: Business & Economics

Page: 646

View: 243

Statistics for Business explains the fundamentals of statistical analysis in a lucid, pragmatic way. A thorough knowledge of statistics is essential for decision making in all corners of business and management. By collecting, organizing and analyzing statistical data you can express what you know, benchmark your current situation, and estimate future outcomes. Based entirely on Microsoft Excel, this book covers a spectrum of statistic fundamentals from basic principles, to probability, sampling, hypothesis testing, forecasting, statistical process control and six-sigma management. This second edition is packed with features to aid understanding and help ensure that every aspect of your knowledge of statistics is applicable to practice, including: Icebreakers introducing each chapter that relate statistics to the real world, drawn from management and hospitality situations Detailed worked examples in each chapter Over 140 case-exercises complete with objective, situation, requirements, and answers A complete glossary of key terminology and formulas, mathematical relationships, and Excel relationships and functions A brand new companion website containing slides, worked-out-solutions to the case-exercises, and a test bank [coming soon] With a clear and accessible style this book makes statistics easier to understand. It is ideal for business, management, tourism and hospitality students who want to learn how to apply statistics to the real world.
Categories: Business & Economics

Recent Advances in Robust Statistics Theory and Applications

Recent Advances in Robust Statistics  Theory and Applications

In the next example, we consider trivariate mixture distributions of normal, Laplace and Student's t with three degrees of freedom, as before with 20 40 60 ...

Author: Claudio Agostinelli

Publisher: Springer

ISBN: 9788132236436

Category: Business & Economics

Page: 201

View: 300

This book offers a collection of recent contributions and emerging ideas in the areas of robust statistics presented at the International Conference on Robust Statistics 2015 (ICORS 2015) held in Kolkata during 12–16 January, 2015. The book explores the applicability of robust methods in other non-traditional areas which includes the use of new techniques such as skew and mixture of skew distributions, scaled Bregman divergences, and multilevel functional data methods; application areas being circular data models and prediction of mortality and life expectancy. The contributions are of both theoretical as well as applied in nature. Robust statistics is a relatively young branch of statistical sciences that is rapidly emerging as the bedrock of statistical analysis in the 21st century due to its flexible nature and wide scope. Robust statistics supports the application of parametric and other inference techniques over a broader domain than the strictly interpreted model scenarios employed in classical statistical methods. The aim of the ICORS conference, which is being organized annually since 2001, is to bring together researchers interested in robust statistics, data analysis and related areas. The conference is meant for theoretical and applied statisticians, data analysts from other fields, leading experts, junior researchers and graduate students. The ICORS meetings offer a forum for discussing recent advances and emerging ideas in statistics with a focus on robustness, and encourage informal contacts and discussions among all the participants. They also play an important role in maintaining a cohesive group of international researchers interested in robust statistics and related topics, whose interactions transcend the meetings and endure year round.
Categories: Business & Economics

The Inverse Gaussian Distribution

The Inverse Gaussian Distribution

This monograph is a compilation of research on the inverse Gaussian distribution. It emphasizes the presentation of the statistical properties, methods, and applications of the two-parameter inverse Gaussian family of distribution.

Author: Raj Chhikara

Publisher: CRC Press

ISBN: 0824779975

Category: Mathematics

Page: 232

View: 865

This monograph is a compilation of research on the inverse Gaussian distribution. It emphasizes the presentation of the statistical properties, methods, and applications of the two-parameter inverse Gaussian family of distribution. It is useful to statisticians and users of statistical distribution.
Categories: Mathematics

Econometric Methods with Applications in Business and Economics

Econometric Methods with Applications in Business and Economics

Example 5.29: Simulated Data of Normal and Student t(2) Distributions To illustrate the idea of robust estimation we consider two data generating processes.

Author: Christiaan Heij

Publisher: OUP Oxford

ISBN: 9780191533235

Category: Business & Economics

Page: 816

View: 327

Nowadays applied work in business and economics requires a solid understanding of econometric methods to support decision-making. Combining a solid exposition of econometric methods with an application-oriented approach, this rigorous textbook provides students with a working understanding and hands-on experience of current econometrics. Taking a 'learning by doing' approach, it covers basic econometric methods (statistics, simple and multiple regression, nonlinear regression, maximum likelihood, and generalized method of moments), and addresses the creative process of model building with due attention to diagnostic testing and model improvement. Its last part is devoted to two major application areas: the econometrics of choice data (logit and probit, multinomial and ordered choice, truncated and censored data, and duration data) and the econometrics of time series data (univariate time series, trends, volatility, vector autoregressions, and a brief discussion of SUR models, panel data, and simultaneous equations). · Real-world text examples and practical exercise questions stimulate active learning and show how econometrics can solve practical questions in modern business and economic management. · Focuses on the core of econometrics, regression, and covers two major advanced topics, choice data with applications in marketing and micro-economics, and time series data with applications in finance and macro-economics. · Learning-support features include concise, manageable sections of text, frequent cross-references to related and background material, summaries, computational schemes, keyword lists, suggested further reading, exercise sets, and online data sets and solutions. · Derivations and theory exercises are clearly marked for students in advanced courses. This textbook is perfect for advanced undergraduate students, new graduate students, and applied researchers in econometrics, business, and economics, and for researchers in other fields that draw on modern applied econometrics.
Categories: Business & Economics

NBS Special Publication

NBS Special Publication

325 BAYESIAN ESTIMATION OF THE VARIANCE OF A NORMAL DISTRIBUTION JRSSB64 63 ... WITH AN APPLICATION TO THE NORMAL DISTRIBUTION CRITERIA FOR BEST SUBSTI JASA ...

Author:

Publisher:

ISBN: UOM:39015023124111

Category: Weights and measures

Page:

View: 566

Categories: Weights and measures

Statistics with Applications in Biology and Geology

Statistics with Applications in Biology and Geology

( 3.93 ) i = 1 If the mean u is replaced by the average 7. ... The distribution is sometimes called the Student distribution or Student'st - distribution .

Author: Preben Blaesild

Publisher: CRC Press

ISBN: 158488309X

Category: Mathematics

Page: 568

View: 597

The use of statistics is fundamental to many endeavors in biology and geology. For students and professionals in these fields, there is no better way to build a statistical background than to present the concepts and techniques in a context relevant to their interests. Statistics with Applications in Biology and Geology provides a practical introduction to using fundamental parametric statistical models frequently applied to data analysis in biology and geology. Based on material developed for an introductory statistics course and classroom tested for nearly 10 years, this treatment establishes a firm basis in models, the likelihood method, and numeracy. The models addressed include one sample, two samples, one- and two-way analysis of variance, and linear regression for normal data and similar models for binomial, multinomial, and Poisson data. Building on the familiarity developed with those models, the generalized linear models are introduced, making it possible for readers to handle fairly complicated models for both continuous and discrete data. Models for directional data are treated as well. The emphasis is on parametric models, but the book also includes a chapter on the most important nonparametric tests. This presentation incorporates the use of the SAS statistical software package, which authors use to illustrate all of the statistical tools described. However, to reinforce understanding of the basic concepts, calculations for the simplest models are also worked through by hand. SAS programs and the data used in the examples and exercises are available on the Internet.
Categories: Mathematics

Probability Inequalities in Multivariate Distributions

Probability Inequalities in Multivariate Distributions

Inequalities on the probability content of convex regions for elliptically ... On certain inequalities for normal distributions and their applications to ...

Author: Y. L. Tong

Publisher: Academic Press

ISBN: 9781483269214

Category: Mathematics

Page: 255

View: 358

Probability Inequalities in Multivariate Distributions is a comprehensive treatment of probability inequalities in multivariate distributions, balancing the treatment between theory and applications. The book is concerned only with those inequalities that are of types T1-T5. The conditions for such inequalities range from very specific to very general. Comprised of eight chapters, this volume begins by presenting a classification of probability inequalities, followed by a discussion on inequalities for multivariate normal distribution as well as their dependence on correlation coefficients. The reader is then introduced to inequalities for other well-known distributions, including the multivariate distributions of t, chi-square, and F; inequalities for a class of symmetric unimodal distributions and for a certain class of random variables that are positively dependent by association or by mixture; and inequalities obtainable through the mathematical tool of majorization and weak majorization. The book also describes some distribution-free inequalities before concluding with an overview of their applications in simultaneous confidence regions, hypothesis testing, multiple decision problems, and reliability and life testing. This monograph is intended for mathematicians, statisticians, students, and those who are primarily interested in inequalities.
Categories: Mathematics

Probability with Statistical Applications

Probability with Statistical Applications

A Student random variable with r degrees of freedom will be denoted by t.r/. Student distributions are very similar to the normal standard distributions: ...

Author: Rinaldo B. Schinazi

Publisher: Springer Science & Business Media

ISBN: 9780817682491

Category: Mathematics

Page: 347

View: 734

This second edition textbook offers a practical introduction to probability for undergraduates at all levels with different backgrounds and views towards applications. Calculus is a prerequisite for understanding the basic concepts, however the book is written with a sensitivity to students’ common difficulties with calculus that does not obscure the thorough treatment of the probability content. The first six chapters of this text neatly and concisely cover the material traditionally required by most undergraduate programs for a first course in probability. The comprehensive text includes a multitude of new examples and exercises, and careful revisions throughout. Particular attention is given to the expansion of the last three chapters of the book with the addition of one entirely new chapter (9) on ’Finding and Comparing Estimators.’ The classroom-tested material presented in this second edition forms the basis for a second course introducing mathematical statistics.
Categories: Mathematics

Statistical Data Analysis for Ocean and Atmospheric Sciences

Statistical Data Analysis for Ocean and Atmospheric Sciences

All told, the normal distributions are basic to an extensive and powerful array of ... Nonetheless, before we immerse ourselves in their application to the ...

Author: H. Jean Thiebaux

Publisher: Elsevier

ISBN: 9780080926292

Category: Mathematics

Page: 247

View: 106

Studies of local and global phenomena generate descriptions which require statistical analysis. In this text, H. Jean Thiebaux presents a succinct yet comprehensive review of the fundamentals of statistics as they pertain to studies in oceanic and atmospheric sciences. The text includes an accompanying disk with compatible Minitab sample data. Together, this volume and the included data provide insights into the basics of statistical inference, data analysis, and distributional models of variability. Oceanographers, meteorologists, marine biologists, and other environmental scientists will find this book of great value as a statistical tool for their continuing studies. Key Features * Specifically designed for students of the ocean and atmospheric sciences * Contains a disk containing files of real ocean and atmospheric data, in universal ASCII format, on which many of the exercises are based * Provides succinct yet comprehensive coverage * Designed to teach students statistical methods with the scientific realism of computer analysis and statistical inference
Categories: Mathematics

Regression Analysis and its Application

Regression Analysis and its Application

The distributions tabulated in this appendix include the cumulative standard normal, cumulative Student t, cumulative chi-square, cumulative F, ...

Author: Richard F. Gunst

Publisher: Routledge

ISBN: 9781351419291

Category: Mathematics

Page: 424

View: 762

Regression Analysis and Its Application: A Data-Oriented Approach answers the need for researchers and students who would like a better understanding of classical regression analysis. Useful either as a textbook or as a reference source, this book bridges the gap between the purely theoretical coverage of regression analysis and its practical application. The book presents regression analysis in the general context of data analysis. Using a teach-by-example format, it contains ten major data sets along with several smaller ones to illustrate the common characteristics of regression data and properties of statistics that are employed in regression analysis. The book covers model misspecification, residual analysis, multicollinearity, and biased regression estimators. It also focuses on data collection, model assumptions, and the interpretation of parameter estimates. Complete with an extensive bibliography, Regression Analysis and Its Application is suitable for statisticians, graduate and upper-level undergraduate students, and research scientists in biometry, business, ecology, economics, education, engineering, mathematics, physical sciences, psychology, and sociology. In addition, data collection agencies in the government and private sector will benefit from the book.
Categories: Mathematics

Data Analysis and Applications 4

Data Analysis and Applications 4

For the distribution F of the series {εt}, we consider in this work (see section 1.3), the normal, the Student-t and the skewed Student-t distribution ([LAM ...

Author: Andreas Makrides

Publisher: John Wiley & Sons

ISBN: 9781119721505

Category: Mathematics

Page: 310

View: 166

Data analysis as an area of importance has grown exponentially, especially during the past couple of decades. This can be attributed to a rapidly growing computer industry and the wide applicability of computational techniques, in conjunction with new advances of analytic tools. This being the case, the need for literature that addresses this is self-evident. New publications are appearing, covering the need for information from all fields of science and engineering, thanks to the universal relevance of data analysis and statistics packages. This book is a collective work by a number of leading scientists, analysts, engineers, mathematicians and statisticians who have been working at the forefront of data analysis. The chapters included in this volume represent a cross-section of current concerns and research interests in these scientific areas. The material is divided into three parts: Financial Data Analysis and Methods, Statistics and Stochastic Data Analysis and Methods, and Demographic Methods and Data Analysis- providing the reader with both theoretical and applied information on data analysis methods, models and techniques and appropriate applications.
Categories: Mathematics