The Birnbaum-Saunders Distribution
The Birnbaum-Saunders Distribution

Author: Victor Leiva

Publisher: Academic Press

Published: 2015-10-26

Total Pages: 156

ISBN-13: 0128038276

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The Birnbaum-Saunders Distribution presents the statistical theory, methodology, and applications of the Birnbaum-Saunders distribution, a very flexible distribution for modeling different types of data (mainly lifetime data). The book describes the most recent theoretical developments of this model, including properties, transformations and related distributions, lifetime analysis, and shape analysis. It discusses methods of inference based on uncensored and censored data, goodness-of-fit tests, and random number generation algorithms for the Birnbaum-Saunders distribution, also presenting existing and future applications. - Introduces inference in the Birnbaum-Saunders distribution - Provides a comprehensive review of the statistical theory and methodology of the Birnbaum-Distribution - Discusses different applications of the Birnbaum-Saunders distribution - Explains characterization and the lifetime analysis

Symmetric and Asymmetric Distributions
Symmetric and Asymmetric Distributions

Author: Emilio Gómez Déniz

Publisher: MDPI

Published: 2021-01-21

Total Pages: 146

ISBN-13: 3039366467

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In recent years, the advances and abilities of computer software have substantially increased the number of scientific publications that seek to introduce new probabilistic modelling frameworks, including continuous and discrete approaches, and univariate and multivariate models. Many of these theoretical and applied statistical works are related to distributions that try to break the symmetry of the normal distribution and other similar symmetric models, mainly using Azzalini's scheme. This strategy uses a symmetric distribution as a baseline case, then an extra parameter is added to the parent model to control the skewness of the new family of probability distributions. The most widespread and popular model is the one based on the normal distribution that produces the skewed normal distribution. In this Special Issue on symmetric and asymmetric distributions, works related to this topic are presented, as well as theoretical and applied proposals that have connections with and implications for this topic. Immediate applications of this line of work include different scenarios such as economics, environmental sciences, biometrics, engineering, health, etc. This Special Issue comprises nine works that follow this methodology derived using a simple process while retaining the rigor that the subject deserves. Readers of this Issue will surely find future lines of work that will enable them to achieve fruitful research results.

First Hitting Time Regression Models
First Hitting Time Regression Models

Author: Chrysseis Caroni

Publisher: John Wiley & Sons

Published: 2017-07-17

Total Pages: 165

ISBN-13: 1119437229

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This book aims to promote regression methods for analyzing lifetime (or time-to-event) data that are based on a representation of the underlying process, and are therefore likely to offer greater scientific insight compared to purely empirical methods. In contrast to the rich statistical literature, the regression methods actually employed in lifetime data analysis are limited, particularly in the biomedical field where D. R. Cox’s famous semi-parametric proportional hazards model predominates. Practitioners should become familiar with more flexible models. The first hitting time regression models (or threshold regression) presented here represent observed events as the outcome of an underlying stochastic process. One example is death occurring when the patient’s health status falls to zero, but the idea has wide applicability – in biology, engineering, banking and finance, and elsewhere. The central topic is the model based on an underlying Wiener process, leading to lifetimes following the inverse Gaussian distribution. Introducing time-varying covariates and many other extensions are considered. Various applications are presented in detail.

Probability Distributions Used in Reliability Engineering
Probability Distributions Used in Reliability Engineering

Author: Andrew N O'Connor

Publisher: RIAC

Published: 2011

Total Pages: 220

ISBN-13: 1933904062

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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.

Testing and Inspection Using Acceptance Sampling Plans
Testing and Inspection Using Acceptance Sampling Plans

Author: Muhammad Aslam

Publisher: Springer

Published: 2019-07-19

Total Pages: 298

ISBN-13: 9811393060

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This book introduces a number of new sampling plans, such as time truncated life tests, skip sampling plans, resubmitted plans, mixed sampling plans, sampling plans based on the process capability index and plans for big data, which can be used for testing and inspecting products, from the raw-materials stage to the final product, in every industry using statistical process control techniques. It also presents the statistical theory, methodology and applications of acceptance sampling from truncated life tests. Further, it discusses the latest reliability, quality and risk analysis methods based on acceptance sampling from truncated life, which engineering and statisticians require in order to make decisions, and which are also useful for researchers in the areas of quality control, lifetime analysis, censored data analysis, goodness-of-fit and statistical software applications. In its nine chapters, the book addresses a wide range of testing/inspection sampling schemes for discrete and continuous data collected in various production processes. It includes a chapter on sampling plans for big data and offers several illustrative examples of the procedures presented. Requiring a basic knowledge of probability distributions, inference and estimation, and lifetime and quality analysis, it is a valuable resource for graduate and senior undergraduate engineering students, and practicing engineers, more specifically it is useful for quality engineers, reliability engineers, consultants, black belts, master black belts, students and researchers interested in applying reliability and risk and quality methods.

Progressive Censoring
Progressive Censoring

Author: N. Balakrishnan

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 255

ISBN-13: 1461213347

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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.

Financial Statistics and Data Analytics
Financial Statistics and Data Analytics

Author: Shuangzhe Li

Publisher: MDPI

Published: 2021-03-02

Total Pages: 232

ISBN-13: 3039439758

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Modern financial management is largely about risk management, which is increasingly data-driven. The problem is how to extract information from the data overload. It is here that advanced statistical and machine learning techniques can help. Accordingly, finance, statistics, and data analytics go hand in hand. The purpose of this book is to bring the state-of-art research in these three areas to the fore and especially research that juxtaposes these three.

System Reliability Theory
System Reliability Theory

Author: Arnljot Høyland

Publisher: John Wiley & Sons

Published: 2009-09-25

Total Pages: 536

ISBN-13: 0470317744

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A comprehensive introduction to reliability analysis. The first section provides a thorough but elementary prologue to reliability theory. The latter half comprises more advanced analytical tools including Markov processes, renewal theory, life data analysis, accelerated life testing and Bayesian reliability analysis. Features numerous worked examples. Each chapter concludes with a selection of problems plus additional material on applications.

The Inverse Gaussian Distribution
The Inverse Gaussian Distribution

Author: V. Seshadri

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 363

ISBN-13: 1461214564

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This book is written in the hope that it will serve as a companion volume to my first monograph. The first monograph was largely devoted to the probabilistic aspects of the inverse Gaussian law and therefore ignored the statistical issues and related data analyses. Ever since the appearance of the book by Chhikara and Folks, a considerable number of publications in both theory and applications of the inverse Gaussian law have emerged thereby justifying the need for a comprehensive treatment of the issues involved. This book is divided into two sections and fills up the gap updating the material found in the book of Chhikara and Folks. Part I contains seven chapters and covers distribution theory, estimation, significance tests, goodness-of-fit, sequential analysis and compound laws and mixtures. The first part forms the backbone of the theory and wherever possible I have provided illustrative examples for easy assimilation of the theory. The second part is devoted to a wide range of applications from various disciplines. The applied statistician will find numerous instances of examples which pertain to a first passage time situation. It is indeed remarkable that in the fields of life testing, ecology, entomology, health sciences, traffic intensity and management science the inverse Gaussian law plays a dominant role. Real life examples from actuarial science and ecology came to my attention after this project was completed and I found it impossible to include them.

An Introduction to Bartlett Correction and Bias Reduction
An Introduction to Bartlett Correction and Bias Reduction

Author: Gauss M. Cordeiro

Publisher: Springer Science & Business Media

Published: 2014-05-08

Total Pages: 113

ISBN-13: 3642552552

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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.