Download or read book Skew Parameter Studies written by Mark R. Wallace and published by . This book was released on 1976 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book STATISTICAL ANALYSIS OF SKEW NORMAL DISTRIBUTION AND ITS APPLICATIONS written by Grace Ngunkeng and published by . This book was released on 2013 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many practical applications it has been observed that real data sets are not symmetric. They exhibit some skewness, therefore do not conform to the normal distribution, which is popular and easy to be handled. Azzalini (1985) introduced a new class of distributions named the skew normal distribution, which is mathematically tractable and includes the normal distribution as a special case with skewness parameter being zero. The skew normal distribution family is well known for modeling and analyzing skewed data. It is the distribution family that extends the normal distribution family by adding a shape parameter to regulate the skewness, which has the higher flexibility in fitting a real data where some skewness is present. In this dissertation, we will explore statistical analysis related to this distribution family. In the first part of the dissertation, we develop a nonparametric goodness-of-fit test based on the empirical likelihood method for the skew normal distribution. The empirical likelihood was proposed by Owen (1988). It is a method which combines the reliability of the canonical nonparametric method with the flexibility and effectiveness of the likelihood approach. The statistical inference of the test statistic is derived. Simulations indicate that the proposed test can control the type I error within a given nominal level, and it has competitive power comparing to the other available tests. The test is applied to IQ scores data set and Australian Institute of Sport data set to illustrate the testing procedure. In the second part we focus on the change point problem of the skew normal distribution. The world is filled with changes, which can lead to unnecessary losses if people are not aware of it. Thus, statisticians are faced with the problem of detecting the number of change points or jumps and their location, in many practical applications. In this part, we address this problem for the standard skew normal family. We focus on the test based on the Schwartz information criterion (SIC) to detect the position and the number of change points for the shape parameter. The likelihood ratio test and the bayesian methods as two alternative approaches will be introduced briefly. The asymptotic null distribution of the SIC test statistics is derived and the critical values for different sample sizes and nominal levels are computed for the adjustified SIC test statistic. Simulation study indicates the performance of the proposed test. In the third part of the dissertation, we extend the methods in the second part by studying the different types of change point problem for the general skew nor mal distribution, which include: the simultaneous changes of location and scale parameters, the simultaneous change of location, scale and shape parameters. We derive the test statistic based on SIC to detect and estimate the number of possible change points. Firstly, we consider the change point problem for the simultaneous changes of location and scale parameters, assuming that the shape parameter is unknown and has to be estimated. Secondly, we explore the change point problem for simultaneous changes of location, scale and shape parameters. The asymptotic null distribution and the corresponding adjustification for the test statistic are established. Simulations for each proposed test are conducted to indicate the performance of the test. Power comparisons with the available tests are investigated to indicate the advantage of the proposed test. Applications to real data are provided to illustrate the test procedure.

Download or read book Skew Normal Model Theories and Their Applications written by Rendao Ye and published by CRC Press. This book was released on 2024-11-08 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book focuses on several skew-normal mixed effects models, and systematically explores statistical inference theories, methods, and applications of parameters of interest. This book is of academic value as it helps to establish a series of statistical inference theories and methods for skew-normal mixed effects models. On the applications side, it provides efficient methods and tools for practical data analysis in various fields including economics, finance, biology and medical science.

Download or read book Graphical Models with R written by Søren Højsgaard and published by Springer Science & Business Media. This book was released on 2012-02-22 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graphical models in their modern form have been around since the late 1970s and appear today in many areas of the sciences. Along with the ongoing developments of graphical models, a number of different graphical modeling software programs have been written over the years. In recent years many of these software developments have taken place within the R community, either in the form of new packages or by providing an R interface to existing software. This book attempts to give the reader a gentle introduction to graphical modeling using R and the main features of some of these packages. In addition, the book provides examples of how more advanced aspects of graphical modeling can be represented and handled within R. Topics covered in the seven chapters include graphical models for contingency tables, Gaussian and mixed graphical models, Bayesian networks and modeling high dimensional data.

Download or read book Finite Mixture and Markov Switching Models written by Sylvia Frühwirth-Schnatter and published by Springer Science & Business Media. This book was released on 2006-11-24 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: The past decade has seen powerful new computational tools for modeling which combine a Bayesian approach with recent Monte simulation techniques based on Markov chains. This book is the first to offer a systematic presentation of the Bayesian perspective of finite mixture modelling. The book is designed to show finite mixture and Markov switching models are formulated, what structures they imply on the data, their potential uses, and how they are estimated. Presenting its concepts informally without sacrificing mathematical correctness, it will serve a wide readership including statisticians as well as biologists, economists, engineers, financial and market researchers.

Download or read book Skew Elliptical Distributions and Their Applications written by Marc G. Genton and published by CRC Press. This book was released on 2004-07-27 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Estimation of the Parameters of Skew Normal Distribution by Approximating the Ratio of the Normal Density and Distribution Functions written by Debarshi Dey and published by . This book was released on 2010 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: The normal distribution is symmetric and enjoys many important properties. That is why it is widely used in practice. Asymmetry in data is a situation where the normality assumption is not valid. Azzalini (1985) introduces the skew normal distribution reflecting varying degrees of skewness. The skew normal distribution is mathematically tractable and includes the normal distribution as a special case. It has three parameters: location, scale and shape. In this thesis we attempt to respond to the complexity and challenges in the maximum likelihood estimates of the three parameters of the skew normal distribution. The complexity is traced to the ratio of the normal density and distribution function in the likelihood equations in the presence of the skewness parameter. Solution to this problem is obtained by approximating this ratio by linear and non-linear functions. We observe that the linear approximation performs quite satisfactorily. In this thesis, we present a method of estimation of the parameters of the skew normal distribution based on this linear approximation. We define a performance measure to evaluate our approximation and estimation method based on it. We present the simulation studies to illustrate the methods and evaluate their performances.

Download or read book Skew Elliptical Distributions and Their Applications written by Marc G. Genton and published by CRC Press. This book was released on 2004-07-27 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 no

Download or read book The Skew Normal and Related Families written by Adelchi Azzalini and published by Cambridge University Press. This book was released on 2014 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: The standard resource for statisticians and applied researchers. Accessible to the wide range of researchers who use statistical modelling techniques.

Download or read book Longitudinal Data Analysis written by Garrett Fitzmaurice and published by CRC Press. This book was released on 2008-08-11 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although many books currently available describe statistical models and methods for analyzing longitudinal data, they do not highlight connections between various research threads in the statistical literature. Responding to this void, Longitudinal Data Analysis provides a clear, comprehensive, and unified overview of state-of-the-art theory

Download or read book Factor Analysis for Skewed Data and Skew Normal Maximum Likelihood Factor Analysis written by Beverly Jane Gaucher and published by . This book was released on 2013 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research explores factor analysis applied to data from skewed distributions for the general skew model, the selection-elliptical model, the selection-normal model, the skew-elliptical model and the skew-normal model for finite sample sizes. In terms of asymptotics, or large sample sizes, quasi-maximum likelihood methods are broached numerically. The skewed models are formed using selection distribution theory, which is based on Rao's weighted distribution theory. The models assume the observed variable of the factor model is from a skewed distribution by defining the distribution of the unobserved common factors skewed and the unobserved unique factors symmetric. Numerical examples are provided using maximum likelihood selection skew-normal factor analysis. The numerical examples, such as maximum likelihood parameter estimation with the resolution of the "sign switching" problem and model fitting using likelihood methods, illustrate that the selection skew-normal factor analysis model better fits skew-normal data than does the normal factor analysis model. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/149548

Download or read book Simplified Live Load Distribution Factor Equations written by BridgeTech, Inc and published by Transportation Research Board. This book was released on 2007 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: This report contains the findings of research performed to develop recommended Load and Resistance Factor Design (LRFD) live load distribution factor design equations for shear and moment. The report details the development of equations that are simpler to apply and have a wider range of applicability than current methods. The appendices are not published in this report, but are available online at http://www.trb.org/news/blurb_detail.asp?id=7938.

Download or read book Measurements of Data Skew in Two Databases written by University of Texas at Austin. Dept. of Computer Sciences and published by . This book was released on 1990 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "Data distributions are presented for relations in two databases: stock trading data and message traffic in a military communications system. This report makes two research contributions. Formal definitions of skew parameters are added to the relative partition model of data skew. Finally, although the observed databases reside on a single node system, skew parameters for three types of data skew are estimated for a worst case partitioning."

Download or read book Shrinkage Estimation written by Dominique Fourdrinier and published by Springer. This book was released on 2018-11-27 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a coherent framework for understanding shrinkage estimation in statistics. The term refers to modifying a classical estimator by moving it closer to a target which could be known a priori or arise from a model. The goal is to construct estimators with improved statistical properties. The book focuses primarily on point and loss estimation of the mean vector of multivariate normal and spherically symmetric distributions. Chapter 1 reviews the statistical and decision theoretic terminology and results that will be used throughout the book. Chapter 2 is concerned with estimating the mean vector of a multivariate normal distribution under quadratic loss from a frequentist perspective. In Chapter 3 the authors take a Bayesian view of shrinkage estimation in the normal setting. Chapter 4 introduces the general classes of spherically and elliptically symmetric distributions. Point and loss estimation for these broad classes are studied in subsequent chapters. In particular, Chapter 5 extends many of the results from Chapters 2 and 3 to spherically and elliptically symmetric distributions. Chapter 6 considers the general linear model with spherically symmetric error distributions when a residual vector is available. Chapter 7 then considers the problem of estimating a location vector which is constrained to lie in a convex set. Much of the chapter is devoted to one of two types of constraint sets, balls and polyhedral cones. In Chapter 8 the authors focus on loss estimation and data-dependent evidence reports. Appendices cover a number of technical topics including weakly differentiable functions; examples where Stein’s identity doesn’t hold; Stein’s lemma and Stokes’ theorem for smooth boundaries; harmonic, superharmonic and subharmonic functions; and modified Bessel functions.

Download or read book Sequential Change point Analysis for Skew Normal Distributions and Nonparametric CUSUM and Shiryaev Roberts Procedures Based on Modified Empirical Likelihood written by Peiyao Wang and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sequential change-point analysis identifies a change of probability distribution in an infinite sequence of observations generated by a process, by repetitively performing a hypothesis test each time a new observation is generated and added to the current data set. It has important applications in many fields, such as financial investment, system monitoring, and quality control. While lots of research have been done for different scenarios, especially time series, few works have been developed for skew data, as well as for the case where the distribution family of observations is unspecified. Hence, in this dissertation, we focus on developing a sequential point detection procedure for the skew-normal distribution family, and a nonparametric procedure based on the modification of previous methods. In the first part of the dissertation, we propose a sequential change-point detection rule for skew-normal distribution, by modifying the procedures proposed by Mei (2006). We focus on the change of location and shape parameters, respectively under the simple and composite alternative hypothesis. We derive the optimality of our modified procedure for location parameter under a simple alternative hypothesis. Also, the simulation shows that our new procedure has fewer false alarms than previous methods when the exact value of pre-change and post-change parameters are not specified. In the second part, we proposed a nonparametric sequential change-point detection procedure, by modifying Page’s CUSUM procedure and the well-known Shiryaev-Roberts (SR) procedure. More specifically, we substitute the parametric likelihood function in the two methods with empirical likelihood (EL), which allows us to perform a likelihood ratio test without knowing the distribution family. Also, we assume training data are available to estimate pre-change and post-change parameters. Different versions of empirical likelihood are applied and simulations are conducted to show their performance. The result shows that compared to previous approaches, such as kernel density estimation, our new method performs better and gives a smaller detection delay when the training sample is small and the underlying distribution is not specified. This is true for both EL-based CUSUM and EL-based SR. Also, EL-based methods are least impacted by the shrinkage of training samples.

Download or read book Predictive Econometrics and Big Data written by Vladik Kreinovich and published by Springer. This book was released on 2017-11-30 with total page 788 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent research on predictive econometrics and big data. Gathering edited papers presented at the 11th International Conference of the Thailand Econometric Society (TES2018), held in Chiang Mai, Thailand, on January 10-12, 2018, its main focus is on predictive techniques – which directly aim at predicting economic phenomena; and big data techniques – which enable us to handle the enormous amounts of data generated by modern computers in a reasonable time. The book also discusses the applications of more traditional statistical techniques to econometric problems. Econometrics is a branch of economics that employs mathematical (especially statistical) methods to analyze economic systems, to forecast economic and financial dynamics, and to develop strategies for achieving desirable economic performance. It is therefore important to develop data processing techniques that explicitly focus on prediction. The more data we have, the better our predictions will be. As such, these techniques are essential to our ability to process huge amounts of available data.

Download or read book The Circuits and Filters Handbook written by Wai-Kai Chen and published by CRC Press. This book was released on 2002-12-23 with total page 3076 pages. Available in PDF, EPUB and Kindle. Book excerpt: A bestseller in its first edition, The Circuits and Filters Handbook has been thoroughly updated to provide the most current, most comprehensive information available in both the classical and emerging fields of circuits and filters, both analog and digital. This edition contains 29 new chapters, with significant additions in the areas of computer-