Download or read book Folded Normal II written by Regina C. Elandt and published by . This book was released on 1961 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt: The general formula for the rth moment of the folded normal distribution is obtained, and formulae for the first four non-central and central moments are calculated explicitly. To illustrate the mode of convergence of teh folded normal to the normal distribution, as [mu]/ơ = [theta] increases, the shape factors ßf1 and ßf2 were calculated and the relationship between them represented graphically. Two methods, one using first and second moments (Method I) and the other using second and fourth moments (Method II) of estimating the parameters of [mu] and ơ of the parent normal distribution are presented and their standard errors calculated. The accuracy of both methods, for various values of [theta], are discussed.

Download or read book The Folded Normal Distribution written by F. C. Leone and published by . This book was released on 1961 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider first the folded normal probability density function, especially as it relates to the original normal population from which it came. We present some maximum likelihood estimates, followed by other estimating procedures which are simpler to handle...Finally, an example of real camber data is presented with the appropriate estimation of the theoretical distributions. Some remarks of the folded normal and other work being done on this conclude the paper.

Download or read book The Folded Normal Distribution Iii Accuracy of Estimation by Maximum Likelihood written by N. L. Johnson and published by . This book was released on 1961 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: Formulae for the asymptotic variances and covariance of the maximum likelihood estimators of the parameters of the folded normal distribution are obtained. Numerical comparisons with the asymptotic variances of moments estimators are made. (Author).

Download or read book An Introductory Handbook of Bayesian Thinking written by Stephen C. Loftus and published by Elsevier. This book was released on 2024-04-17 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: As Bayesian techniques become more common across a variety of fields, it becomes important for experts in those fields to understand those methods. An Introductory Handbook of Bayesian Thinking brings Bayesian thinking and methods to a wide audience beyond the mathematical sciences. Appropriate for students with some background in calculus and introductory statistics, particularly for nonstatisticians with a sufficient mathematical background, the text provides a gentle introduction to Bayesian ideas with a wide array of supporting examples from a variety of fields. Utilizes real datasets to illustrate Bayesian models and their results Guides readers on coding Bayesian models using the statistical software R, including a helpful introduction and supporting online resource Appropriate for an undergraduate statistics course, as well as for non-statisticians with sufficient mathematical background (integral and differential Calculus and an introductory Statistics course) Covers any more advanced topics which readers may not be familiar with—such as the basic idea of vectors and matrices—as much as needed in order to foster understanding of core concepts

Download or read book Normal and Student s t Distributions and Their Applications written by Mohammad Ahsanullah and published by Springer Science & Business Media. This book was released on 2014-02-07 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Handbook of Multivariate Process Capability Indices written by Ashis Kumar Chakraborty and published by CRC Press. This book was released on 2021-01-20 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing a single-valued assessment of the performance of a process is often one of the greatest challenges for a quality professional. Process Capability Indices (PCIs) precisely do this job. For processes having a single measurable quality characteristic, there is an ample number of PCIs, defined in literature. The situation worsens for multivariate processes, i.e., where there is more than one correlated quality characteristic. Since in most situations quality professionals face multiple quality characteristics to be controlled through a process, Multivariate Process Capability Indices (MPCIs) become the order of the day. However, there is no book which addresses and explains different MPCIs and their properties. The literature of Multivariate Process Capability Indices (MPCIs) is not well organized, in the sense that a thorough and systematic discussion on the various MPCIs is hardly available in the literature. Handbook of Multivariate Process Capability Indices provides an extensive study of the MPCIs defined for various types of specification regions. This book is intended to help quality professionals to understand which MPCI should be used and in what situation. For researchers in this field, the book provides a thorough discussion about each of the MPCIs developed to date, along with their statistical and analytical properties. Also, real life examples are provided for almost all the MPCIs discussed in the book. This helps both the researchers and the quality professionals alike to have a better understanding of the MPCIs, which otherwise become difficult to understand, since there is more than one quality characteristic to be controlled at a time. Features: A complete guide for quality professionals on the usage of different MPCIs. A step by step discussion on multivariate process capability analysis, starting from a brief discussion on univariate indices. A single source for all kinds of MPCIs developed so far. Comprehensive analysis of the MPCIs, including analysis of real-life data. References provided at the end of each chapter encompass the entire literature available on the respective topic. Interpretation of the MPCIs and development of threshold values of many MPCIs are also included. This reference book is aimed at the post graduate students in Industrial Statistics. It will also serve researchers working in the field of Industrial Statistics, as well as practitioners requiring thorough guidance regarding selection of an appropriate MPCI suitable for the problem at hand.

Download or read book Sensitivity Analysis in Linear Regression written by Samprit Chatterjee and published by John Wiley & Sons. This book was released on 1988-03-31 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Treats linear regression diagnostics as a tool for application of linear regression models to real-life data. Presentation makes extensive use of examples to illustrate theory. Assesses the effect of measurement errors on the estimated coefficients, which is not accounted for in a standard least squares estimate but is important where regression coefficients are used to apportion effects due to different variables. Also assesses qualitatively and numerically the robustness of the regression fit.

Download or read book Multiple Decision Procedures written by Shanti S. Gupta and published by SIAM. This book was released on 1979-01-01 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiple Decision Procedures: Theory and Methodology of Selecting and Ranking Populations provides an encyclopedic coverage of the literature in the area of ranking and selection procedures, summarizing and surveying in a unified manner a majority of more than 600 main references in the bibliography. It also deals with related problems, such as the estimation of unknown ordered parameters. A separate chapter is devoted to information about several tables available in the literature for carrying out various specific procedures. Examples are given in another chapter illustrating applications of these procedures in various practical contexts. Although several books have appeared to date in this area, many of them deal with specific aspects of the field and a limited number of topics. This book contains substantial material not discussed in other books. Audience: this book can serve as a text for a graduate topics course in ranking and selection (as it has done at Purdue University for more than 30 years). It can also serve as a reference for researchers and practitioners in fields such as agriculture, industry, engineering, and behavioral sciences.

Download or read book Continuous Multivariate Distributions Volume 1 written by Samuel Kotz and published by John Wiley & Sons. This book was released on 2004-04-05 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuous Multivariate Distributions, Volume 1, Second Edition provides a remarkably comprehensive, self-contained resource for this critical statistical area. It covers all significant advances that have occurred in the field over the past quarter century in the theory, methodology, inferential procedures, computational and simulational aspects, and applications of continuous multivariate distributions. In-depth coverage includes MV systems of distributions, MV normal, MV exponential, MV extreme value, MV beta, MV gamma, MV logistic, MV Liouville, and MV Pareto distributions, as well as MV natural exponential families, which have grown immensely since the 1970s. Each distribution is presented in its own chapter along with descriptions of real-world applications gleaned from the current literature on continuous multivariate distributions and their applications.

Download or read book Non Standard Parametric Statistical Inference written by Russell Cheng and published by Oxford University Press. This book was released on 2017 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the fitting of parametric statistical models to data samples. Emphasis is placed on: (i) how to recognize situations where the problem is non-standard when parameter estimates behave unusually, and (ii) the use of parametric bootstrap resampling methods in analyzing such problems. A frequentist likelihood-based viewpoint is adopted, for which there is a well-established and very practical theory. The standard situation is where certain widely applicable regularity conditions hold. However, there are many apparently innocuous situations where standard theory breaks down, sometimes spectacularly. Most of the departures from regularity are described geometrically, with only sufficient mathematical detail to clarify the non-standard nature of a problem and to allow formulation of practical solutions. The book is intended for anyone with a basic knowledge of statistical methods, as is typically covered in a university statistical inference course, wishing to understand or study how standard methodology might fail. Easy to understand statistical methods are presented which overcome these difficulties, and demonstrated by detailed examples drawn from real applications. Simple and practical model-building is an underlying theme. Parametric bootstrap resampling is used throughout for analyzing the properties of fitted models, illustrating its ease of implementation even in non-standard situations. Distributional properties are obtained numerically for estimators or statistics not previously considered in the literature because their theoretical distributional properties are too hard to obtain theoretically. Bootstrap results are presented mainly graphically in the book, providing an accessible demonstration of the sampling behaviour of estimators.

Download or read book Benchmarking for Performance Evaluation written by Subhash C. Ray and published by Springer. This book was released on 2015-03-25 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed introduction to the theoretical and methodological foundations of production efficiency analysis using benchmarking. Two of the more popular methods of efficiency evaluation are Stochastic Frontier Analysis (SFA) and Data Envelopment Analysis (DEA), both of which are based on the concept of a production possibility set and its frontier. Depending on the assumed objectives of the decision-making unit, a Production, Cost, or Profit Frontier is constructed from observed data on input and output quantities and prices. While SFA uses different maximum likelihood estimation techniques to estimate a parametric frontier, DEA relies on mathematical programming to create a nonparametric frontier. Yet another alternative is the Convex Nonparametric Frontier, which is based on the assumed convexity of the production possibility set and creates a piecewise linear frontier consisting of a number of tangent hyper planes. Three of the papers in this volume provide a detailed and relatively easy to follow exposition of the underlying theory from neoclassical production economics and offer step-by-step instructions on the appropriate model to apply in different contexts and how to implement them. Of particular appeal are the instructions on (i) how to write the codes for different SFA models on STATA, (ii) how to write a VBA Macro for repetitive solution of the DEA problem for each production unit on Excel Solver, and (iii) how to write the codes for the Nonparametric Convex Frontier estimation. The three other papers in the volume are primarily theoretical and will be of interest to PhD students and researchers hoping to make methodological and conceptual contributions to the field of nonparametric efficiency analysis.

Download or read book Statistics for Process Control Engineers written by Myke King and published by John Wiley & Sons. This book was released on 2017-08-10 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first statistics guide focussing on practical application to process control design and maintenance Statistics for Process Control Engineers is the only guide to statistics written by and for process control professionals. It takes a wholly practical approach to the subject. Statistics are applied throughout the life of a process control scheme – from assessing its economic benefit, designing inferential properties, identifying dynamic models, monitoring performance and diagnosing faults. This book addresses all of these areas and more. The book begins with an overview of various statistical applications in the field of process control, followed by discussions of data characteristics, probability functions, data presentation, sample size, significance testing and commonly used mathematical functions. It then shows how to select and fit a distribution to data, before moving on to the application of regression analysis and data reconciliation. The book is extensively illustrated throughout with line drawings, tables and equations, and features numerous worked examples. In addition, two appendices include the data used in the examples and an exhaustive catalogue of statistical distributions. The data and a simple-to-use software tool are available for download. The reader can thus reproduce all of the examples and then extend the same statistical techniques to real problems. Takes a back-to-basics approach with a focus on techniques that have immediate, practical, problem-solving applications for practicing engineers, as well as engineering students Shows how to avoid the many common errors made by the industry in applying statistics to process control Describes not only the well-known statistical distributions but also demonstrates the advantages of applying the large number that are less well-known Inspires engineers to identify new applications of statistical techniques to the design and support of control schemes Provides a deeper understanding of services and products which control engineers are often tasked with assessing This book is a valuable professional resource for engineers working in the global process industry and engineering companies, as well as students of engineering. It will be of great interest to those in the oil and gas, chemical, pulp and paper, water purification, pharmaceuticals and power generation industries, as well as for design engineers, instrument engineers and process technical support.

Download or read book Statistical Properties of the Generalized Inverse Gaussian Distribution written by B. Jorgensen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1978 the idea of studying the generalized inverse Gaussian distribution was proposed to me by Professor Ole Barndorff-Nielsen, who had come across the distribution in the study of the socalled hyperbolic distributions where it emerged in connection with the representation of the hyperbolic distributions as mixtures of normal distributions. The statistical properties of the generalized inverse Gaussian distribution were at that time virtually unde veloped, but it turned out that the distribution has some nice properties, and models many sets of data satisfactorily. This work contains an account of the statistical properties of the distribu tion as far as they are developed at present. The work was done at the Department of Theoretical Statistics, Aarhus University, mostly in 1979, and was partial fulfilment to wards my M. Sc. degree. I wish to convey my warm thanks to Ole Barn dorff-Nielsen and Preben BI~sild for their advice and for comments on earlier versions of the manuscript and to Jette Hamborg for her skilful typing.

Download or read book Stability Problems for Stochastic Models Theory and Applications written by Alexander Zeifman and published by MDPI. This book was released on 2021-03-05 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this Special Issue of Mathematics is to commemorate the outstanding Russian mathematician Vladimir Zolotarev, whose 90th birthday will be celebrated on February 27th, 2021. The present Special Issue contains a collection of new papers by participants in sessions of the International Seminar on Stability Problems for Stochastic Models founded by Zolotarev. Along with research in probability distributions theory, limit theorems of probability theory, stochastic processes, mathematical statistics, and queuing theory, this collection contains papers dealing with applications of stochastic models in modeling of pension schemes, modeling of extreme precipitation, construction of statistical indicators of scientific publication importance, and other fields.

Download or read book Active Evaluation of Predictive Models written by Christoph Sawade and published by Universitätsverlag Potsdam. This book was released on 2013 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Practitioner s Guide to Stochastic Frontier Analysis Using Stata written by Subal C. Kumbhakar and published by Cambridge University Press. This book was released on 2015-01-26 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Practitioner's Guide to Stochastic Frontier Analysis Using Stata provides practitioners in academia and industry with a step-by-step guide on how to conduct efficiency analysis using the stochastic frontier approach. The authors explain in detail how to estimate production, cost, and profit efficiency and introduce the basic theory of each model in an accessible way, using empirical examples that demonstrate the interpretation and application of models. This book also provides computer code, allowing users to apply the models in their own work, and incorporates the most recent stochastic frontier models developed in academic literature. Such recent developments include models of heteroscedasticity and exogenous determinants of inefficiency, scaling models, panel models with time-varying inefficiency, growth models, and panel models that separate firm effects and persistent and transient inefficiency. Immensely helpful to applied researchers, this book bridges the chasm between theory and practice, expanding the range of applications in which production frontier analysis may be implemented.

Download or read book The Theory of Probability written by Santosh S. Venkatesh and published by Cambridge University Press. This book was released on 2013 with total page 830 pages. Available in PDF, EPUB and Kindle. Book excerpt: From classical foundations to modern theory, this comprehensive guide to probability interweaves mathematical proofs, historical context and detailed illustrative applications.