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.
Author(s): Gauss M. Cordeiro, Rodrigo B. Silva, Abraão D.C. Nascimento
Publisher: Bentham Science Publishers
Year: 2020
Language: English
Pages: 249
City: Sharjah
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
