应力-强度模型及其广义化
2003-12
Penguin
Samuel Kotz 著
253
The applied case studies strengthen the reader's interest, understanding, and appreciation of the concepts.
PrefaceChapter 1 The Stress-Strength Models. Mathematics,History, and Applications 1.1 What are the Stress-Strength Models? 1.2 Motivation and Mathematical Formulations 1.2.1 Motivations 1.2.2 Mathematical Formulations 1.3 Stress-Strength Models: History and Geography 1.3.1 History 1.3.2 Geography 1.4 ApplicationsChapter 2 The Theory and Some Useful Approaches 2.1 The Maximum Likelihood Estimators 2.1.1 The Theory 2.1.2 Construction of the MLE 2.1.3 One-parameter Exponential Distribution 2.1.4 Multivariate Case 2.2 Unbiased Estimation 2.2.1 The Theory 2.2.2 Construction of UMVUEs 2.2.3 One-parameter Exponential Distribution 2.2.4 A Multivariate Case 2.3 Bayes and Empirical Bayes Estimation of R 2.3.1 The Theory 2.3.2 The Choice of a Prior 2.3.3 One-parameter Exponential Distribution 2.3.4 Bayes Predictive and Empirical Bayes Estimation 2.4 Interval Estimation 2.4.1 The Theory 2.4.2 Exact Methods of Interval Estimation 2.4.3 Asymptotic Methods of Interval Estimation 2.4.4 Bayesian Credible Sets 2.4.5 Hypothesis Testing: Theory and Methods 2.4.6 One-parameter Exponential Distribution 2.5 Transformation Methods 2.5.1 The Theory 2.5.2 Examples of Transformations 2.5.3 The Rayleigh Distribution 2.6 ExercisesChapter 3 Parametric Point Estimation 3.1 The Maximum Likelihood Estimation (Univariate Case) 3.1.1 The Normal Distribution 3.1.2 The Two-parameter Exponential Distribution 3.1.3 The Gamma Distribution 3.1.4 The Truncation Parameter Families 3.1.5 The Pareto Distribution 3.1.6 The Weibull Distribution 3.1.7 Burr Type X and Type XII Distributions 3.1.8 The Generalized Gamma Distribution 3.1.9 Other Distributions 3.2 Unbiased Estimation (Univariate Case) 3.2.1 The Normal Distribution 3.2.2 The Two-parameter Exponential Distribution 3.2.3 The Gamma Distribution 3.2.4 The Truncation Parameter Families 3.2.5 The Generalized Gamma Distribution 3.2.6 Other Distributions 3.3 Bayes and Empirical Bayes Estimation (Univariate Case) 3.3.1 The Normal Distribution 3.3.2 The One-Parameter Exponential Distribution ……Chapter 4 Parametric Statistical InferenceChapter 5 Nonparametric ModelsChapter 6 Some Selected Special Cases Chapter 7 Applications and ExamplesBibliographyIndex
