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Bias Of The Maximum Likelihood Estimator Of The Generalized Rayleigh Distribution
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Book Synopsis Bias of the Maximum Likelihood Estimator of the Generalized Rayleigh Distribution by : Xiao Ling
Download or read book Bias of the Maximum Likelihood Estimator of the Generalized Rayleigh Distribution written by Xiao Ling and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We derive analytic expressions for the biases, to O(n-1) of the maximum likelihood estimators of the parameters of the generalized Rayleigh distribution family. Using these expressions to bias-correct the estimators is found to be extremely effective in terms of bias reduction, and generally results in a small reduction in relative mean squared error. In general, the analytic bias-corrected estimators are also found to be superior to the alternative of bias-correction via the bootstrap.
Book Synopsis Weighted Generalization of Rayleigh and Related Class of Distributions by : Xueheng Shi
Download or read book Weighted Generalization of Rayleigh and Related Class of Distributions written by Xueheng Shi and published by . This book was released on 2011 with total page 59 pages. Available in PDF, EPUB and Kindle. Book excerpt: Author's abstract: Weighted distributions occur naturally and frequently in research related to reliability, bio-medicine, ecology and in the modeling of clustered sample, heterogeneity, and extraneous variation. In the analysis of intervention data, the expected value of the duration to completion of a random event sampled randomly at the end of its duration turns out to be approximately equal to the expected duration of its random interventions. This is due to the concept of size or length-biased sampling, where the weight function represents the duration of the random event in the life cycle assessment. The case of chronic disease identified by early detection screening programs constitute a length biased (weighted) sampling procedure, as individuals with a long pre-clinical disease phase have a greater probability of being identified. In this research, a new weighted generalization of the Raleigh distribution is constructed. The construction makes use of the "conservability approach" which includes the size or length-biased distribution as a special case. Weighted generalized Raleigh distribution (WGRD) with several weight functions are constructed. The properties of these distributions including behavior of hazard or failure rate and reverse hazard functions, moments, moment generating function, mean, variance, coefficient of variation, coefficient of skewness, coefficient of kurtosis are obtained. Other important properties including entropy (Shannon, beta and generalized) which are measures of the uncertainty in these distributions, and Fisher information which measures the amount of information that a random variable carries about the distribution's unknown parameters are derived and studied. Estimation of the parameters of the weighted generalized Raleigh distribution including the maximum likelihood estimators are derived. Test procedures for weightedness including length-biasedness concerning the Raleigh, generalized Raleigh and weighted generalized Raleigh models are developed.
Book Synopsis Progressive Censoring by : N. Balakrishnan
Download or read book Progressive Censoring written by N. Balakrishnan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new book offers a guide to the theory and methods of progressive censoring. In many industrial experiments involving lifetimes of machines or units, experiments have to be terminated early. Progressive Censoring first introduces progressive sampling foundations, and then discusses various properties of progressive samples. The book points out the greater efficiency gained by using this scheme instead of classical right-censoring methods.
Book Synopsis Methods for Statistical Analysis of Reliability and Life Data by : Nancy R. Mann
Download or read book Methods for Statistical Analysis of Reliability and Life Data written by Nancy R. Mann and published by . This book was released on 1974 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Introduction to Bartlett Correction and Bias Reduction by : Gauss M. Cordeiro
Download or read book An Introduction to Bartlett Correction and Bias Reduction written by Gauss M. Cordeiro and published by Springer Science & Business Media. This book was released on 2014-05-08 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a concise introduction to Bartlett and Bartlett-type corrections of statistical tests and bias correction of point estimators. The underlying idea behind both groups of corrections is to obtain higher accuracy in small samples. While the main focus is on corrections that can be analytically derived, the authors also present alternative strategies for improving estimators and tests based on bootstrap, a data resampling technique and discuss concrete applications to several important statistical models.
Book Synopsis Biases and Covariances of Maximum Likelihood Estimators by : Kimiko Osada Bowman
Download or read book Biases and Covariances of Maximum Likelihood Estimators written by Kimiko Osada Bowman and published by . This book was released on 1965 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Microelectronics, Electromagnetics and Telecommunications by : P. Satish Rama Chowdary
Download or read book Microelectronics, Electromagnetics and Telecommunications written by P. Satish Rama Chowdary and published by Springer Nature. This book was released on 2020-06-24 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the latest developments and outlines future trends in the fields of microelectronics, electromagnetics and telecommunication. It includes original research presented at the International Conference on Microelectronics, Electromagnetics and Telecommunication (ICMEET 2019), organized by the Department of ECE, Raghu Institute of Technology, Andhra Pradesh, India. Written by scientists, research scholars and practitioners from leading universities, engineering colleges and R&D institutes around the globe, the papers share the latest breakthroughs in and promising solutions to the most important issues facing today’s society.
Book Synopsis The Stress-strength Model and Its Generalizations by : Samuel Kotz
Download or read book The Stress-strength Model and Its Generalizations written by Samuel Kotz and published by World Scientific. This book was released on 2003 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important book presents developments in a remarkable field ofinquiry in statistical/probability theory the stressOCostrengthmodel.Many papers in the field include the enigmatic words"P"("X"Y") or something similar in thetitle."
Book Synopsis A Parameter Estimation Technique for the Generalized Rayleigh-Rician Distribution and Laha's Bessel Distribution by :
Download or read book A Parameter Estimation Technique for the Generalized Rayleigh-Rician Distribution and Laha's Bessel Distribution written by and published by . This book was released on 1976 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this report is to provide a means by which the parameters of the generalized Rayleigh distribution can be estimated from experimental data. This report is an outgrowth of research in the area of laser radar technology; however, the results should be of general interest and find application in other disciplines where the generalized Rayleigh distribution is encountered.
Book Synopsis Probability and Statistics for Engineering and the Sciences, Enhanced Review Edition by : Jay Devore
Download or read book Probability and Statistics for Engineering and the Sciences, Enhanced Review Edition written by Jay Devore and published by Cengage Learning. This book was released on 2008-01-29 with total page 768 pages. Available in PDF, EPUB and Kindle. Book excerpt: This market-leading text provides a comprehensive introduction to probability and statistics for engineering students in all specialties. This proven, accurate book and its excellent examples evidence Jay Devore’s reputation as an outstanding author and leader in the academic community. Devore emphasizes concepts, models, methodology, and applications as opposed to rigorous mathematical development and derivations. Through the use of lively and realistic examples, students go beyond simply learning about statistics-they actually put the methods to use. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
Download or read book Data written by David F. Andrews and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistics provides tools and strategies for the analysis of data. While much has been written about the methodology, sometimes without reference to data, little has been said about the data. In this volume we present sets of data obtained from many situations without any direct reference to a particular type of analysis. Our view of the usefulness of bringing together a broad collection of sets of data has been shared by many friends and contributors. Students of statistics need to gain facility with their art by applying their knowledge to many sets of data. Textbook examples tend to be small and selected primarily to illustrate a particular technique, thus failing to demonstrate the questioning, iterative nature of statistical analysis. The situations which gave rise to the more extensive sets of data given in this volume are colourful and interesting, and can be readily understood by laymen, students and research workers with diverse interests. These sets were often chosen for their perverse reluctance to yield under the naive application of standard procedures. They do not have correct solutions. They describe situations where the statisti cian can develop skills and learn the limitations of statistical methods.
Book Synopsis Using the Weibull Distribution by : John I. McCool
Download or read book Using the Weibull Distribution written by John I. McCool and published by John Wiley & Sons. This book was released on 2012-08-06 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understand and utilize the latest developments in Weibull inferential methods While the Weibull distribution is widely used in science and engineering, most engineers do not have the necessary statistical training to implement the methodology effectively. Using the Weibull Distribution: Reliability, Modeling, and Inference fills a gap in the current literature on the topic, introducing a self-contained presentation of the probabilistic basis for the methodology while providing powerful techniques for extracting information from data. The author explains the use of the Weibull distribution and its statistical and probabilistic basis, providing a wealth of material that is not available in the current literature. The book begins by outlining the fundamental probability and statistical concepts that serve as a foundation for subsequent topics of coverage, including: • Optimum burn-in, age and block replacement, warranties and renewal theory • Exact inference in Weibull regression • Goodness of fit testing and distinguishing the Weibull from the lognormal • Inference for the Three Parameter Weibull Throughout the book, a wealth of real-world examples showcases the discussed topics and each chapter concludes with a set of exercises, allowing readers to test their understanding of the presented material. In addition, a related website features the author's own software for implementing the discussed analyses along with a set of modules written in Mathcad®, and additional graphical interface software for performing simulations. With its numerous hands-on examples, exercises, and software applications, Using the Weibull Distribution is an excellent book for courses on quality control and reliability engineering at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for engineers, scientists, and business analysts who gather and interpret data that follows the Weibull distribution
Book Synopsis Probability Distributions Used in Reliability Engineering by : Andrew N O'Connor
Download or read book Probability Distributions Used in Reliability Engineering written by Andrew N O'Connor and published by RIAC. This book was released on 2011 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides details on 22 probability distributions. Each distribution section provides a graphical visualization and formulas for distribution parameters, along with distribution formulas. Common statistics such as moments and percentile formulas are followed by likelihood functions and in many cases the derivation of maximum likelihood estimates. Bayesian non-informative and conjugate priors are provided followed by a discussion on the distribution characteristics and applications in reliability engineering.
Book Synopsis Rethinking Biased Estimation by : Yonina C. Eldar
Download or read book Rethinking Biased Estimation written by Yonina C. Eldar and published by Now Publishers Inc. This book was released on 2008 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rethinking Biased Estimation discusses methods to improve the accuracy of unbiased estimators used in many signal processing problems. At the heart of the proposed methodology is the use of the mean-squared error (MSE) as the performance criteria. One of the prime goals of statistical estimation theory is the development of performance bounds when estimating parameters of interest in a given model, as well as constructing estimators that achieve these limits. When the parameters to be estimated are deterministic, a popular approach is to bound the MSE achievable within the class of unbiased estimators. Although it is well-known that lower MSE can be obtained by allowing for a bias, in applications it is typically unclear how to choose an appropriate bias. Rethinking Biased Estimation introduces MSE bounds that are lower than the unbiased Cramer-Rao bound (CRB) for all values of the unknowns. It then presents a general framework for constructing biased estimators with smaller MSE than the standard maximum-likelihood (ML) approach, regardless of the true unknown values. Specializing the results to the linear Gaussian model, it derives a class of estimators that dominate least-squares in terms of MSE. It also introduces methods for choosing regularization parameters in penalized ML estimators that outperform standard techniques such as cross validation.
Book Synopsis Weibull Models by : D. N. Prabhakar Murthy
Download or read book Weibull Models written by D. N. Prabhakar Murthy and published by John Wiley & Sons. This book was released on 2004-01-28 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive perspective on Weibull models The literature on Weibull models is vast, disjointed, andscattered across many different journals. Weibull Models is acomprehensive guide that integrates all the different facets ofWeibull models in a single volume. This book will be of great help to practitioners in reliabilityand other disciplines in the context of modeling data sets usingWeibull models. For researchers interested in these modelingtechniques, exercises at the end of each chapter define potentialtopics for future research. Organized into seven distinct parts, Weibull Models: * Covers model analysis, parameter estimation, model validation,and application * Serves as both a handbook and a research monograph. As ahandbook, it classifies the different models and presents theirproperties. As a research monograph, it unifies the literature andpresents the results in an integrated manner * Intertwines theory and application * Focuses on model identification prior to model parameterestimation * Discusses the usefulness of the Weibull Probability plot (WPP)in the model selection to model a given data set * Highlights the use of Weibull models in reliability theory Filled with in-depth analysis, Weibull Models pulls together themost relevant information on this topic to give everyone fromreliability engineers to applied statisticians involved withreliability and survival analysis a clear look at what Weibullmodels can offer.
Book Synopsis Generalized Principal Component Analysis by : René Vidal
Download or read book Generalized Principal Component Analysis written by René Vidal and published by Springer. This book was released on 2016-04-11 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to the latest advances in the mathematical theory and computational tools for modeling high-dimensional data drawn from one or multiple low-dimensional subspaces (or manifolds) and potentially corrupted by noise, gross errors, or outliers. This challenging task requires the development of new algebraic, geometric, statistical, and computational methods for efficient and robust estimation and segmentation of one or multiple subspaces. The book also presents interesting real-world applications of these new methods in image processing, image and video segmentation, face recognition and clustering, and hybrid system identification etc. This book is intended to serve as a textbook for graduate students and beginning researchers in data science, machine learning, computer vision, image and signal processing, and systems theory. It contains ample illustrations, examples, and exercises and is made largely self-contained with three Appendices which survey basic concepts and principles from statistics, optimization, and algebraic-geometry used in this book. René Vidal is a Professor of Biomedical Engineering and Director of the Vision Dynamics and Learning Lab at The Johns Hopkins University. Yi Ma is Executive Dean and Professor at the School of Information Science and Technology at ShanghaiTech University. S. Shankar Sastry is Dean of the College of Engineering, Professor of Electrical Engineering and Computer Science and Professor of Bioengineering at the University of California, Berkeley.
Book Synopsis Discrete Choice Methods with Simulation by : Kenneth Train
Download or read book Discrete Choice Methods with Simulation written by Kenneth Train and published by Cambridge University Press. This book was released on 2009-07-06 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the new generation of discrete choice methods, focusing on the many advances that are made possible by simulation. Researchers use these statistical methods to examine the choices that consumers, households, firms, and other agents make. Each of the major models is covered: logit, generalized extreme value, or GEV (including nested and cross-nested logits), probit, and mixed logit, plus a variety of specifications that build on these basics. Simulation-assisted estimation procedures are investigated and compared, including maximum stimulated likelihood, method of simulated moments, and method of simulated scores. Procedures for drawing from densities are described, including variance reduction techniques such as anithetics and Halton draws. Recent advances in Bayesian procedures are explored, including the use of the Metropolis-Hastings algorithm and its variant Gibbs sampling. The second edition adds chapters on endogeneity and expectation-maximization (EM) algorithms. No other book incorporates all these fields, which have arisen in the past 25 years. The procedures are applicable in many fields, including energy, transportation, environmental studies, health, labor, and marketing.
