Main Data
Author: Roberto Minguez, Jose-Maria Sarabia, N. Balakrishnan, Barry C Arnold
Editor: Barry Arnold, N Balakrishnan, Jose Maria Sarabia, Roberto Minguez
Title: Advances in Mathematical and Statistical Modeling
Publisher: Birkhäuser Basel
ISBN/ISSN: 9780817646264
Edition: 1
Price: CHF 119.00
Publication date: 01/01/2009
Category: Informatik, EDV Buch
Language: English
Technical Data
Pages: 368
Kopierschutz: DRM
Geräte: PC/MAC/eReader/Tablet
Formate: PDF
Table of contents

Enrique Castillo is a leading figure in several mathematical and engineering fields. Organized to honor Castillo's significant contributions, this volume is an outgrowth of the 'International Conference on Mathematical and Statistical Modeling,' and covers recent advances in the field. Applications to safety, reliability and life-testing, financial modeling, quality control, general inference, as well as neural networks and computational techniques are presented.

Table of contents
List of Contributors21
List of Tables26
List of Figures29
Part I Distribution Theory and Applications32
1 Enrique Castillos Contributions to Conditional Specification33
1.1 Introduction33
1.2 Conditionals in Given Exponential Families34
1.3 Conditionals in Given Non-Exponential Families38
1.4 Truncated and Weighted Distributions39
1.5 A Digression on Improper Models39
1.6 Characterizations of Classical Models Via Conditional Specifications40
1.7 Back to the Bayesian Scenario40
1.8 Inference for Conditionally Specified Models41
1.9 Incomplete and Imprecise Conditional Specification41
1.10 Future Prospects47
2 The Polygonal Distribution50
2.1 Introduction50
2.2 The Triangular Distribution51
2.3 The Polygonal Distribution52
2.4 The Polygonal Distribution as a Mixing Density55
2.5 Discussion61
3 Conditionally Specified Models: New Developments and Applications63
3.1 Introduction63
3.2 Bivariate Power Conditionals Distribution64
3.3 Mixture Conditional Models with Applications to Actuarial Statistics66
3.4 Bivariate Income Distributions67
3.5 Flexible Conjugate Prior Families67
3.6 Conditional Hazard Functions69
4 Modelling of Insurance Claim Count with Hurdle Distribution for Panel Data72
4.1 Introduction72
4.2 Cross Section versus Panel Data74
4.3 Poisson Distribution75
4.4 Hurdle Models76
4.5 Predictive Distribution80
4.6 Insurance Application82
4.7 Conclusion85
5 Distance-Based Association and Multi-Sample Tests for General Multivariate Data87
5.1 Introduction87
5.2 Multivariate Association88
5.3 The Proximity Function90
5.4 The Distance-based Bayes Allocation Rule91
5.5 Multivariate Multiple-Sample Tests92
Part II Probability and Statistics98
6 Empirical Bayes Assessment of the Hyperparameters in Bayesian Factor Analysis99
6.1 Introduction99
6.2 The BFA Model100
6.3 Assessing the Hyperparameters101
6.4 Bayesian Estimation of ., F, .103
6.5 Example105
6.6 Method Comparison and Summary108
Part III Order Statistics and Analysis110
7 Negative Mixtures, Order Statistics, and Systems111
7.1 Introduction111
7.2 Relationships between Mixtures and Systems112
7.3 Properties of Mixtures and Systems114
7.4 The Bridge Structure117
8 Models of Ordered Data and Products of Beta Random Variables123
8.1 Introduction123
8.2 Intermediate Order Statistics and the Ordered Dirichlet Distribution125
8.3 Properties of Fractional Order Statistics127
9 Exact Inference and Optimal Censoring Scheme for a Simple Step- Stress Model Under Progressive Type- II Censoring129
9.1 Introduction129
9.2 Model Description and MLEs131
9.3 Conditional Distributions of the MLEs133
9.4 Confidence Intervals139
9.5 Simulation Study143
9.6 Optimal Censoring Scheme143
9.7 Illustrative Examples145
9.8 Conclusions147
Appendix: Tables and Figures148
Part IV Engineering Modeling160
10 Non-Gaussian State Estimation in Power Systems161
10.1 Introduction161
10.2 Maximum Likelihood Estimation162
10.3 Transformation of Random Variables163
10.4 The Transformed Likelihood Estimation Problem166
10.5 General State Estimation (GSE) Formulation167
10.6 Bad Data Detection168
10.7 Illustrative Example168
10.8 Conclusions174
11 Statistics Applied to Wave Climate on a Beach Profile177
11.1 Introduction177
11.2 Offshore Wave Climate178
11.3 Local Wave Height Description181
11.4 Consecutive Wave Heights184
11.5 Maximum Wave Height186
11.6 Conclusions188
Part V Extreme Value Theory189
12 On Some Dependence Measures for Multivariate Extreme Value Distributions190
12.1 Introduction190
12.2 Dependence Coefficients191
12.3 Examples193
12.4 Relation between t1 and t2195