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Advances in Mathematical and Statistical Modeling

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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 123.20
Publication date:	01/01/2009

Content

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

	Contents	8
	Preface	17
	List of Contributors	21
	List of Tables	26
	List of Figures	29
	Part I Distribution Theory and Applications	32
	1 Enrique Castillos Contributions to Conditional Specification	33
	1.1 Introduction	33
	1.2 Conditionals in Given Exponential Families	34
	1.3 Conditionals in Given Non-Exponential Families	38
	1.4 Truncated and Weighted Distributions	39
	1.5 A Digression on Improper Models	39
	1.6 Characterizations of Classical Models Via Conditional Specifications	40
	1.7 Back to the Bayesian Scenario	40
	1.8 Inference for Conditionally Specified Models	41
	1.9 Incomplete and Imprecise Conditional Specification	41
	1.10 Future Prospects	47
	References	47
	2 The Polygonal Distribution	50
	2.1 Introduction	50
	2.2 The Triangular Distribution	51
	2.3 The Polygonal Distribution	52
	2.4 The Polygonal Distribution as a Mixing Density	55
	2.5 Discussion	61
	References	61
	3 Conditionally Specified Models: New Developments and Applications	63
	3.1 Introduction	63
	3.2 Bivariate Power Conditionals Distribution	64
	3.3 Mixture Conditional Models with Applications to Actuarial Statistics	66
	3.4 Bivariate Income Distributions	67
	3.5 Flexible Conjugate Prior Families	67
	3.6 Conditional Hazard Functions	69
	References	70
	4 Modelling of Insurance Claim Count with Hurdle Distribution for Panel Data	72
	4.1 Introduction	72
	4.2 Cross Section versus Panel Data	74
	4.3 Poisson Distribution	75
	4.4 Hurdle Models	76
	4.5 Predictive Distribution	80
	4.6 Insurance Application	82
	4.7 Conclusion	85
	References	85
	5 Distance-Based Association and Multi-Sample Tests for General Multivariate Data	87
	5.1 Introduction	87
	5.2 Multivariate Association	88
	5.3 The Proximity Function	90
	5.4 The Distance-based Bayes Allocation Rule	91
	5.5 Multivariate Multiple-Sample Tests	92
	References	96
	Part II Probability and Statistics	98
	6 Empirical Bayes Assessment of the Hyperparameters in Bayesian Factor Analysis	99
	6.1 Introduction	99
	6.2 The BFA Model	100
	6.3 Assessing the Hyperparameters	101
	6.4 Bayesian Estimation of ., F, .	103
	6.5 Example	105
	6.6 Method Comparison and Summary	108
	References	109
	Part III Order Statistics and Analysis	110
	7 Negative Mixtures, Order Statistics, and Systems	111
	7.1 Introduction	111
	7.2 Relationships between Mixtures and Systems	112
	7.3 Properties of Mixtures and Systems	114
	7.4 The Bridge Structure	117
	Appendix	120
	References	121
	8 Models of Ordered Data and Products of Beta Random Variables	123
	8.1 Introduction	123
	8.2 Intermediate Order Statistics and the Ordered Dirichlet Distribution	125
	8.3 Properties of Fractional Order Statistics	127
	References	128
	9 Exact Inference and Optimal Censoring Scheme for a Simple Step- Stress Model Under Progressive Type- II Censoring	129
	9.1 Introduction	129
	9.2 Model Description and MLEs	131
	9.3 Conditional Distributions of the MLEs	133
	9.4 Confidence Intervals	139
	9.5 Simulation Study	143
	9.6 Optimal Censoring Scheme	143
	9.7 Illustrative Examples	145
	9.8 Conclusions	147
	Appendix: Tables and Figures	148
	References	158
	Part IV Engineering Modeling	160
	10 Non-Gaussian State Estimation in Power Systems	161
	10.1 Introduction	161
	10.2 Maximum Likelihood Estimation	162
	10.3 Transformation of Random Variables	163
	10.4 The Transformed Likelihood Estimation Problem	166
	10.5 General State Estimation (GSE) Formulation	167
	10.6 Bad Data Detection	168
	10.7 Illustrative Example	168
	10.8 Conclusions	174
	References	175
	11 Statistics Applied to Wave Climate on a Beach Profile	177
	11.1 Introduction	177
	11.2 Offshore Wave Climate	178
	11.3 Local Wave Height Description	181
	11.4 Consecutive Wave Heights	184
	11.5 Maximum Wave Height	186
	11.6 Conclusions	188
	References	188
	Part V Extreme Value Theory	189
	12 On Some Dependence Measures for Multivariate Extreme Value Distributions	190
	12.1 Introduction	190
	12.2 Dependence Coefficients	191
	12.3 Examples	193
	12.4 Relation between t1 and t2	195