Chi-Squared Goodness of Fit Tests with Applications provides a thorough and complete context for the theoretical basis and implementation of Pearson s monumental contribution and its wide applicability for chi-squared goodness of fit tests. The book is ideal for researchers and scientists conducting statistical analysis in processing of experimental data as well as to students and practitioners with a good mathematical background who use statistical methods. The historical context, especially Chapter 7, provides great insight into importance of this subject with an authoritative author team. This reference includes the most recent application developments in using these methods and models.
Systematic presentation with interesting historical context and coverage of the fundamentals of the subjectPresents modern model validity methods, graphical techniques, and computer-intensive methodsRecent research and a variety of open problemsInteresting real-life examples for practitioners"

The book is a selection of invited chapters, all of which deal with various aspects of mathematical and statistical models and methods in reliability. Written by renowned experts in the field of reliability, the contributions cover a wide range of applications, reflecting recent developments in areas such as survival analysis, aging, lifetime data analysis, artificial intelligence, medicine, carcinogenesis studies, nuclear power, financial modeling, aircraft engineering, quality control, and transportation.

"Mathematical and Statistical Models and Methods in Reliability" is an excellent reference text for researchers and practitioners in applied probability and statistics, industrial statistics, engineering, medicine, finance, transportation, the oil and gas industry, and artificial intelligence.

Statistical inferential methods are widely used in the study of various physical, biological, social, and other phenomena. Parametric estimation is one such method. Although there are many books which consider problems of statistical point estimation, this volume is the first to be devoted solely to the problem of unbiased estimation. It contains three chapters dealing, respectively, with the theory of point statistical estimation, techniques for constructing unbiased estimators, and applications of unbiased estimation theory. These chapters are followed by a comprehensive appendix which classifies and lists, in the form of tables, all known results relating to unbiased estimators of parameters for univariate distributions. About one thousand minimum variance unbiased estimators are listed. The volume also contains numerous examples and exercises. 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 graduate students.

1 Reliability: Past, Present, Future.- 2 Reliability Analysis as a Tool for Expressing and Communicating Uncertainty.- 3 Modeling a Process of Non-Ideal Repair.- 4 Some Models and Mathematical Results for Reliability of Systems of Components.- 5 Algorithms of Stochastic Activity and Problems of Reliability.- 6 Some Shifted Stochastic Orders.- 7 Characterization of Distributions in Reliability.- 8 Asymptotic Analysis of Reliability for Switching Systems in Light and Heavy Traffic Conditions.- 9 Nonlinearly Perturbed Markov Chains and Large Deviations for Lifetime Functionals.- 10 Evolutionary Systems in an Asymptotic Split Phase Space.- 11 An Asymptotic Approach to Multistate Systems Reliability Evaluation.- 12 Computer Intensive Methods Based on Resampling in Analysis of Reliability and Survival Data.- 13 Statistical Analysis of Damage Processes.- 14 Data Analysis Based on Warranty Database.- 15 Failure Models Indexed by Time and Usage.- 16 A New Multiple Proof Loads Approach For Estimating Correlations.- 17 Conditional and Partial Correlation For Graphical Uncertainty Models.- 18 Semiparametric Methods of Time Scale Selection.- 19 Censored and Truncated Lifetime Data.- 20 Tests for a Family of Survival Models Based on Extremes.- 21 Software Reliability Models - Past, Present and Future.- 22 Dynamic Analysis of Failures in Repairable Systems and Software.- 23 Precedence Test and Maximal Precedence Test.- 24 Hierarchical Bayesian Inference in Related Reliability Experiments.- 25 Tests for Equality of Intensities of Failures of a Repairable System Under Two Competing Risks.- 26 Semiparametric Estimation in Accelerated Life Testing.- 27 A Theoretical Framework for Accelerated Testing.- 28 Unbiased Estimation in Reliability and Similar Problems.- 29 Prediction Under Association.- 30 Uniform Limit Laws for Kernel Density Estimators on Possibly Unbounded Intervals.- 31 A Weak Convergence Result Relevant in Recurrent and Renewal Models.

Parametric and semiparametric models are tools with a wide range of applications to reliability, survival analysis, and quality of life. This self-contained volume examines these tools in survey articles written by experts currently working on the development and evaluation of models and methods. While a number of chapters deal with general theory, several explore more specific connections and recent results in "real-world" reliability theory, survival analysis and related fields.

Specific topics covered include:

* non-parametric estimation of lifetimes of subjects exposed to radiation

* statistical analysis of simultaneous degradation-mortality data with covariates of the aged

* estimation of maintenance efficiency in semiparametric imperfect repair models

* cancer prognosis using survival forests

* short-term health problems related to air pollution: analysis using semiparametric generalized additive models

* parametric models in accelerated life testing and fuzzy data

* semiparametric models in the studies of aging and longevity

This book will be of use as a reference text for general statisticians, theoreticians, graduate students, reliability engineers, health researchers, and biostatisticians working in applied probability and statistics.

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.

This volume dedicated to William Q. Meeker on the occasion of his sixtieth birthday is a collection of invited chapters covering recent advances in accelerated life testing and degradation models. The book covers a wide range of applications to areas such as reliability, quality control, the health sciences, economics and finance. Additional topics covered include accelerated testing and inference, step-stress testing and inference, nonparametric inference, model validity in accelerated testing, the point process approach, bootstrap methods in degradation analysis, exact inferential methods in reliability, dynamic perturbed systems, and degradation models in statistics. Advances in Degradation Modeling is an excellent reference for researchers and practitioners in applied probability and statistics, industrial statistics, the health sciences, quality control, economics, and finance.

Probability, Statistics and Modelling in Public Health consists of refereed contributions by expert biostatisticians that discuss various probabilistic and statistical models used in public health. Many of them are based on the work of Marvin Zelen of the Harvard School of Public Health. Topics discussed include models based on Markov and semi-Markov processes, multi-state models, models and methods in lifetime data analysis, accelerated failure models, design and analysis of clinical trials, Bayesian methods, pharmaceutical and environmental statistics, degradation models, epidemiological methods, screening programs, early detection of diseases, and measurement and analysis of quality of life.

The 37 expository articles in this volume provide broad coverage of important topics relating to the theory, methods, and applications of goodness-of-fit tests and model validity. The book is divided into eight parts, each of which presents topics written by expert researchers in their areas. Key features include: * state-of-the-art exposition of modern model validity methods, graphical techniques, and computer-intensive methods * systematic presentation with sufficient history and coverage of the fundamentals of the subject * exposure to recent research and a variety of open problems * many interesting real life examples for practitioners * extensive bibliography, with special emphasis on recent literature * subject index This comprehensive reference work will serve the statistical and applied mathematics communities as well as practitioners in the field.

This book deals with the mathematical aspects of survival analysis and reliability as well as other topics, reflecting recent developments in the following areas: applications in epidemiology; probabilistic and statistical models and methods in reliability; models and methods in survival analysis, longevity, aging, and degradation; accelerated life models; quality of life; new statistical challenges in genomics.

The work will be useful to a broad interdisciplinary readership of researchers and practitioners in applied probability and statistics, industrial statistics, biomedicine, biostatistics, and engineering.

This book presents thirty-one extensive and carefully edited chapters providing an up-to-date survey of new models and methods for reliability analysis and applications in science, engineering, and technology. The chapters contain broad coverage of the latest developments and innovative techniques in a wide range of theoretical and numerical issues in the field of statistical and probabilistic methods in reliability.

Statistical inferential methods are widely used in the study of various physical, biological, social, and other phenomena. Parametric estimation is one such method. Although there are many books which consider problems of statistical point estimation, this volume is the first to be devoted solely to the problem of unbiased estimation. It contains three chapters dealing, respectively, with the theory of point statistical estimation, techniques for constructing unbiased estimators, and applications of unbiased estimation theory. These chapters are followed by a comprehensive appendix which classifies and lists, in the form of tables, all known results relating to unbiased estimators of parameters for univariate distributions. About one thousand minimum variance unbiased estimators are listed. The volume also contains numerous examples and exercises. 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 graduate students.

The 37 expository articles in this volume provide broad coverage of important topics relating to the theory, methods, and applications of goodness-of-fit tests and model validity. The book is divided into eight parts, each of which presents topics written by expert researchers in their areas. Key features include: * state-of-the-art exposition of modern model validity methods, graphical techniques, and computer-intensive methods * systematic presentation with sufficient history and coverage of the fundamentals of the subject * exposure to recent research and a variety of open problems * many interesting real life examples for practitioners * extensive bibliography, with special emphasis on recent literature * subject index This comprehensive reference work will serve the statistical and applied mathematics communities as well as practitioners in the field.

Probability, Statistics and Modelling in Public Health consists of refereed contributions by expert biostatisticians that discuss various probabilistic and statistical models used in public health. Many of them are based on the work of Marvin Zelen of the Harvard School of Public Health. Topics discussed include models based on Markov and semi-Markov processes, multi-state models, models and methods in lifetime data analysis, accelerated failure models, design and analysis of clinical trials, Bayesian methods, pharmaceutical and environmental statistics, degradation models, epidemiological methods, screening programs, early detection of diseases, and measurement and analysis of quality of life.

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.

Parametric and semiparametric models are tools with a wide range of applications to reliability, survival analysis, and quality of life. This self-contained volume examines these tools in survey articles written by experts currently working on the development and evaluation of models and methods. While a number of chapters deal with general theory, several explore more specific connections and recent results in "real-world" reliability theory, survival analysis, and related fields. Specific topics covered include: * cancer prognosis using survival forests * short-term health problems related to air pollution: analysis using semiparametric generalized additive models * semiparametric models in the studies of aging and longevity This book will be of use as a reference text for general statisticians, theoreticians, graduate students, reliability engineers, health researchers, and biostatisticians working in applied probability and statistics.

This book is devoted to the problems of construction and application of chi-squared goodness-of-fit tests for complete and censored data. Classical chi-squared tests assume that unknown distribution parameters are estimated using grouped data, but in practice this assumption is often forgotten. In this book, we consider modified chi-squared tests, which do not suffer from such a drawback. The authors provide examples of chi-squared tests for various distributions widely used in practice, and also consider chi-squared tests for the parametric proportional hazards model and accelerated failure time model, which are widely used in reliability and survival analysis. Particular attention is paid to the choice of grouping intervals and simulations. This book covers recent innovations in the field as well as important results previously only published in Russian. Chi-squared tests are compared with other goodness-of-fit tests (such as the Cramer-von Mises-Smirnov, Anderson-Darling and Zhang tests) in terms of power when testing close competing hypotheses.