Author: Xiao Ling Publisher: ISBN: Category : Languages : en Pages :
Book Description
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.
Author: Xueheng Shi Publisher: ISBN: Category : Electronic dissertations Languages : en Pages : 59
Book Description
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.
Author: N. Balakrishnan Publisher: Springer Science & Business Media ISBN: 1461213347 Category : Mathematics Languages : en Pages : 255
Book Description
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.
Author: Publisher: ISBN: Category : Languages : en Pages : 26
Book Description
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.
Author: P. Satish Rama Chowdary Publisher: Springer Nature ISBN: 981153828X Category : Technology & Engineering Languages : en Pages : 762
Book Description
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.
Author: Gauss M. Cordeiro Publisher: Springer Science & Business Media ISBN: 3642552552 Category : Mathematics Languages : en Pages : 113
Book Description
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.
Author: Samuel Kotz Publisher: World Scientific ISBN: 9789812564511 Category : Mathematics Languages : en Pages : 276
Book Description
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."
Author: Yonina C. Eldar Publisher: Now Publishers Inc ISBN: 1601981309 Category : Mathematics Languages : en Pages : 159
Book Description
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.
Author: Xiao Ling
Author: Xueheng Shi
Author: N. Balakrishnan
Author: Kimiko Osada Bowman
Author: 
Author: P. Satish Rama Chowdary
Author: Gauss M. Cordeiro
Author: Samuel Kotz
Author: Yonina C. Eldar
Author: