The Birnbaum-Saunders distribution

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 distributionProvides a comprehensive review of the statistical theory and methodology of the Birnbaum-DistributionDiscusses different applications of the Birnbaum-Saunders distributionExplains characterization and the lifetime analysis The Birnbaum-Saunders distribution is a very flexible model for describing different types of data. There have recently been diverse developments of this distribution, including properties, moments, simulation, inference, modeling, diagnostics, goodness of fit and novel applications The objective of this book is to provide an overview of the Birnbaum-Saunders distribution and its probabilistic and statistical features, as well as its goodness of fit and extension to regression analysis and diagnostics A differentiating aspect of this book is the presentation of codes in the R statistical software The book starts by introducing life distributions and detailing the genesis of the Birnbaum-Saunders distribution Then, it provides its characterizations, simulation, inference, modeling, diagnostics, goodness of fit and real-world data analyses. Chapter 2 goes on to characterize relevant properties, moments, and simulation aspects Chapter 3 discusses inference and different estimation methods. Chapter 4 formulates regression models and their diagnostics Chapter 5 introduces goodness-of-fit methods Finally, Chapter 6 shows examples of how to carry out real-world data analyses with the aid of the R software The Birnbaum-Saunders Distribution is a comprehensive review of its statistical theory, modeling, and applications. Book jacket. This book presents the statistical theory, methodology and applications of the Birnbaum-Saunders distribution, which is a very flexible distribution for modeling different type 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, the book presents some applications. Introduces inference in the Birnbaum-Saunders distribution Discusses different applications of the Birnbaum-Saunders distribution Explains characterization and the life time analysis.

MSC 60Exx ; 62Exx.

1 Genesis 1.1 Introduction 1.2 History 1.3 Fatigue, genesis and derivation 1.4 Applications 2 Characterizations 2.1 Introduction 2.2 Probability functions and properties 2.3 Characteristic function and moments 2.4 Generation of random numbers 3 Inference 3.1 Introduction 3.2 Maximum likelihood estimation method 3.3 Moment estimation method 3.4 Graphical estimation method 4 Modelling 4.1 Introduction 4.2 The logarithmic Birnbaum-Saunders distribution 4.3 Regression models 4.4 Diagnostics methods 5 Data analysis and fitting 5.1 Introduction 5.2 Goodness-of-fit based on moments 5.3 Goodness-of-fit based on probability plots 5.4 Data analysis.