Recent Advances in Lifetime and Reliability Models

Description

Mathematicians and statisticians have made significant academic progress on the subject of distribution theory in the last two decades, and this area of study is becoming one of the main statistical tools for the analysis of lifetime (survival) data. In many ways, lifetime distributions are the common language of survival dialogue because the framework subsumes many statistical properties of interest, such as reliability, entropy and maximum likelihood.Recent Advances in Lifetime and Reliability Models provides a comprehensive account of models and methods for lifetime models. Building from primary definitions such as density and hazard rate functions, this book presents readers a broad framework on distribution theory in survival analysis. This framework covers classical methods - such as the exponentiated distribution method – as well as recent models explaining lifetime distributions, such as the beta family and compounding models. Additionally, a detailed discussion of mathematical and statistical properties of each family, such as mixture representations, asymptotes, types of moments, order statistics, quantile functions, generating functions and estimation is presented in the book.Key Features:- presents information about classical and modern lifetime methods- covers key properties of different models in detail- explores regression models for the beta generalized family of distributions- focuses information on both theoretical fundamentals and practical aspects of implementing different models- features examples relevant to business engineering and biomedical sciencesRecent Advances in Lifetime and Reliability Models will equip students, researchers and working professionals with the information to make extensive use of observational data in a variety of fields to create inferential models that make sense of lifetime data. Cover Title Copyright End User License Agreement Contents Foreword Preface Introduction PRIMARY DEFINITIONS CENSORING KINDS First Censoring Second Censoring Parametric Estimation in Failure Data SURVIVAL REGRESSION MODEL Cox Proportional Hazards Model Accelerated Failure Time Model SPECIAL FUNCTIONS STATISTICAL FUNCTIONS Exponentiated Models INTRODUCTION SPECIAL CASES The EE Distribution The EW Distribution ORDINARY MOMENTS The EE Distribution The EW Distribution OTHER MOMENTS The EE Distribution The EW Distribution INCOME MEASURES The EE Distribution The EW Distribution ORDER STATISTICS For the EE Distribution For the EW Distribution ENTROPY The EE Distribution The EW Distribution ESTIMATION For the EE Distribution For the EW Distribution APPLICATION CONCLUSIONS Beta Generalized Models INTRODUCTION SOME SPECIAL MODELS QUANTILE FUNCTION USEFUL EXPANSIONS MOMENTS SOME BASELINE PWMs PWMs of the Beta Gamma PWMs of the Beta Normal PWMs of the Beta Beta PWMs of the Beta Student t PWMs BASED ON QUANTILES Moments of the Beta Gamma Moments of the Beta Student t Moments of the Beta Beta GENERATING FUNCTION MEAN DEVIATIONS ORDER STATISTICS RELIABILITY ENTROPY ESTIMATION BETA-G REGRESSION MODEL An Extended Weibull Distribution The Log-extended Weibull Distribution The Log-extended Weibull Regression Model CONCLUSIONS Special Generalized Beta Models BETA GENERALIZED EXPONENTIAL BETA WEIBULL BETA FRÉCHET BETA MODIFIED WEIBULL BETA BIRNBAUM-SAUNDERS APPLICATIONS CONCLUSIONS The Kumaraswamy's Generalized Family of Models INTRODUCTION PHYSICAL MOTIVATION SPECIAL Kw-G DISTRIBUTIONS Kw-Normal (KwN) Kw-Weibull (KwW) Kw-Gamma (KwG) Kw-Gumbel (KwGu) Kw-Inverse Gaussian (KwIG) Kw-Chen (KwChen) Kw-XTG (KwXTG) Kw-Flexible Weibull (KwFW) ASYMPTOTES AND SHAPES SIMULATION USEFUL EXPANSIONS MOMENTS GENERATING FUNCTION MEAN DEVIATIONS RELATION WITH THE BETA-G ESTIMATION CONCLUSIONS Special Kumaraswamy Generalized Models KUMARASWAMY WEIBULL Linear Representation Moments Generating Function Maximum Likelihood Estimation Applications KUMARASWAMY BURR XII Expansion for the Density Function Moments Generating Function Estimation Simulation Studies Applications KUMARASWAMY GUMBEL Distribution and Density Functions Shapes Moments Generating Function Maximum Likelihood Estimation Bootstrap Re-sampling Methods A Bayesian Analysis Application: Minimum Flow Data CONCLUSIONS The Gamma-G Family of Distributions INTRODUCTION SPECIAL GAMMA-G MODELS The Gamma-Weibull Distribution The Gamma-Normal Distribution The Gamma-Gumbel Distribution The Gamma-lognormal Distribution The Gamma-log-logistic Distribution LINEAR REPRESENTATIONS ASYMPTOTES and SHAPES QUANTILE FUNCTION MOMENTS GENERATING FUNCTION MEAN DEVIATIONS ENTROPIES ORDER STATISTICS LIKELIHOOD ESTIMATION A BIVARIATE GENERALIZATION APPLICATION THE RISTIC AND BALAKRISHNAN FAMILY ESTIMATION AND APPLICATION CONCLUSIONS Recent Compounding Models INTRODUCTION QUANTILE FUNCTION USEFUL EXPANSIONS OTHER QUANTITIES ORDER STATISTICS ESTIMATION APPLICATIONS CONCLUSIONS Conclusions and Recent Advances Bibliography Subject Index Back Cover