Arnold / Minguez / Balakrishnan Advances in Mathematical and Statistical Modeling

1. Auflage 2009
ISBN: 978-0-8176-4626-4
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 368 Seiten

Reihe: Statistics for Industry and Technology

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.

Autoren/Hrsg.

Minguez, Roberto

Sarabia, Jose-Maria

Balakrishnan, N.

Arnold, Barry C.

Sarabia Alegria, Jose-Maria

Inhaltsverzeichnis

1;Contents;8
2;Preface;17
3;List of Contributors;21
4;List of Tables;26
5;List of Figures;29
6;Part I Distribution Theory and Applications;32
6.1;1 Enrique Castillo’s Contributions to Conditional Specification;33
6.1.1;1.1 Introduction;33
6.1.2;1.2 Conditionals in Given Exponential Families;34
6.1.3;1.3 Conditionals in Given Non-Exponential Families;38
6.1.4;1.4 Truncated and Weighted Distributions;39
6.1.5;1.5 A Digression on Improper Models;39
6.1.6;1.6 Characterizations of Classical Models Via Conditional Specifications;40
6.1.7;1.7 Back to the Bayesian Scenario;40
6.1.8;1.8 Inference for Conditionally Specified Models;41
6.1.9;1.9 Incomplete and Imprecise Conditional Specification;41
6.1.10;1.10 Future Prospects;47
6.1.11;References;47
6.2;2 The Polygonal Distribution;50
6.2.1;2.1 Introduction;50
6.2.2;2.2 The Triangular Distribution;51
6.2.3;2.3 The Polygonal Distribution;52
6.2.4;2.4 The Polygonal Distribution as a Mixing Density;55
6.2.5;2.5 Discussion;61
6.2.6;References;61
6.3;3 Conditionally Specified Models: New Developments and Applications;63
6.3.1;3.1 Introduction;63
6.3.2;3.2 Bivariate Power Conditionals Distribution;64
6.3.3;3.3 Mixture Conditional Models with Applications to Actuarial Statistics;66
6.3.4;3.4 Bivariate Income Distributions;67
6.3.5;3.5 Flexible Conjugate Prior Families;67
6.3.6;3.6 Conditional Hazard Functions;69
6.3.7;References;70
6.4;4 Modelling of Insurance Claim Count with Hurdle Distribution for Panel Data;72
6.4.1;4.1 Introduction;72
6.4.2;4.2 Cross Section versus Panel Data;74
6.4.3;4.3 Poisson Distribution;75
6.4.4;4.4 Hurdle Models;76
6.4.5;4.5 Predictive Distribution;80
6.4.6;4.6 Insurance Application;82
6.4.7;4.7 Conclusion;85
6.4.8;References;85
6.5;5 Distance-Based Association and Multi-Sample Tests for General Multivariate Data;87
6.5.1;5.1 Introduction;87
6.5.2;5.2 Multivariate Association;88
6.5.3;5.3 The Proximity Function;90
6.5.4;5.4 The Distance-based Bayes Allocation Rule;91
6.5.5;5.5 Multivariate Multiple-Sample Tests;92
6.5.6;References;96
7;Part II Probability and Statistics;98
7.1;6 Empirical Bayes Assessment of the Hyperparameters in Bayesian Factor Analysis;99
7.1.1;6.1 Introduction;99
7.1.2;6.2 The BFA Model;100
7.1.3;6.3 Assessing the Hyperparameters;101
7.1.4;6.4 Bayesian Estimation of ., F, .;103
7.1.5;6.5 Example;105
7.1.6;6.6 Method Comparison and Summary;108
7.1.7;References;109
8;Part III Order Statistics and Analysis;110
8.1;7 Negative Mixtures, Order Statistics, and Systems;111
8.1.1;7.1 Introduction;111
8.1.2;7.2 Relationships between Mixtures and Systems;112
8.1.3;7.3 Properties of Mixtures and Systems;114
8.1.4;7.4 The Bridge Structure;117
8.1.5;Appendix;120
8.1.6;References;121
8.2;8 Models of Ordered Data and Products of Beta Random Variables;123
8.2.1;8.1 Introduction;123
8.2.2;8.2 Intermediate Order Statistics and the Ordered Dirichlet Distribution;125
8.2.3;8.3 Properties of Fractional Order Statistics;127
8.2.4;References;128
8.3;9 Exact Inference and Optimal Censoring Scheme for a Simple Step- Stress Model Under Progressive Type- II Censoring;129
8.3.1;9.1 Introduction;129
8.3.2;9.2 Model Description and MLEs;131
8.3.3;9.3 Conditional Distributions of the MLEs;133
8.3.4;9.4 Confidence Intervals;139
8.3.5;9.5 Simulation Study;143
8.3.6;9.6 Optimal Censoring Scheme;143
8.3.7;9.7 Illustrative Examples;145
8.3.8;9.8 Conclusions;147
8.3.9;Appendix: Tables and Figures;148
8.3.10;References;158
9;Part IV Engineering Modeling;160
9.1;10 Non-Gaussian State Estimation in Power Systems;161
9.1.1;10.1 Introduction;161
9.1.2;10.2 Maximum Likelihood Estimation;162
9.1.3;10.3 Transformation of Random Variables;163
9.1.4;10.4 The Transformed Likelihood Estimation Problem;166
9.1.5;10.5 General State Estimation (GSE) Formulation;167
9.1.6;10.6 Bad Data Detection;168
9.1.7;10.7 Illustrative Example;168
9.1.8;10.8 Conclusions;174
9.1.9;References;175
9.2;11 Statistics Applied to Wave Climate on a Beach Profile;177
9.2.1;11.1 Introduction;177
9.2.2;11.2 Offshore Wave Climate;178
9.2.3;11.3 Local Wave Height Description;181
9.2.4;11.4 Consecutive Wave Heights;184
9.2.5;11.5 Maximum Wave Height;186
9.2.6;11.6 Conclusions;188
9.2.7;References;188
10;Part V Extreme Value Theory;189
10.1;12 On Some Dependence Measures for Multivariate Extreme Value Distributions;190
10.1.1;12.1 Introduction;190
10.1.2;12.2 Dependence Coefficients;191
10.1.3;12.3 Examples;193
10.1.4;12.4 Relation between t1 and t2;195
10.1.5;12.5 Combining Two Independent Models;198
10.1.6;References;199
10.2;13 Ratio of Maximum to the Sum for Testing Super Heavy Tails;200
10.2.1;13.1 Introduction;200
10.2.2;13.2 Main Results;202
10.2.3;13.3 Simulation Results and Real Data Analysis;203
10.2.4;13.4 Auxiliary Results;207
10.2.5;13.5 Proofs;208
10.2.6;References;212
10.3;14 Tail Behaviour: An Empirical Study;214
10.3.1;14.1 Introduction;214
10.3.2;14.2 Asymptotic CI’s for the Tail Index and the VaR;216
10.3.3;14.3 Reduced Bias Tail Index and Quantile Estimators;217
10.3.4;14.4 An Algorithm for Semi-Parametric Tail Estimation;219
10.3.5;14.5 The Use of a Parametric Quantile Method in Tail Index and Quantile Estimation;220
10.3.6;14.6 Financial Data Analysis;222
10.3.7;References;225
10.4;15 An Example of Real–Life Data Where the Hill Estimator is Correct;227
10.4.1;15.1 Introduction;227
10.4.2;15.2 The Pareto Modeling;228
10.4.3;15.3 The Hill Estimator;229
10.4.4;15.4 Modified Pickands Estimators;230
10.4.5;15.5 Analyzing the Long Term Copepod Data;231
10.4.6;15.6 Computational Aspects;233
10.4.7;References;233
11;Part VI Business and Economics Applications;235
11.1;16 Deriving Credibility Premiums Under Different Bayesian Methodology;236
11.1.1;16.1 Introduction;236
11.1.2;16.2 Classical Model of Bühlmann;238
11.1.3;16.3 Standard Bayesian Credibility;239
11.1.4;16.4 Credibility Based on Robust Bayesian Analysis;240
11.1.5;16.5 Beyond the Loss Function;243
11.1.6;16.6 Discussion;245
11.1.7;References;245
11.2;17 The Influence of Transport Links on Disaggregation and Regionalization Methods in Interregional Input- Output Models Between Metropolitan and Remote Areas;247
11.2.1;17.1 Introduction;247
11.2.2;17.2 Methodology;248
11.2.3;17.3 Results and Discussion;252
11.2.4;17.4 Conclusions;256
11.2.5;References;256
12;Part VII Statistical Methods;258
12.1;18 Jackknife Bias Correction of a Clock Offset Estimator;259
12.1.1;18.1 Introduction;259
12.1.2;18.2 Candidate Clock Offset Estimators;261
12.1.3;18.3 Mean Squared Error Under Exponential and Pareto Distributions;262
12.1.4;18.4 Additional Mean Squared Error Comparisons via Simulation;264
12.1.5;18.5 Summary;267
12.1.6;References;268
12.2;19 Pretesting in Polytomous Logistic Regression Models Based on Phi- divergence Measures;269
12.2.1;19.1 Introduction;269
12.2.2;19.2 Preliminaries and Notation;271
12.2.3;19.3 Contiguous Alternative Hypotheses;273
12.2.4;19.4 Asymptotic Distributional Quadratic Risk of ßf2, ßH0f2 and ßpref1,f2;276
12.2.5;19.5 Comparison of ßf2, ßH0f2 and ßpref1,f2;278
12.2.6;References;279
12.3;20 A Unified Approach to Model Selection, Discrimination, Goodness of Fit and Outliers in Time Series;280
12.3.1;20.1 Introduction;280
12.3.2;20.2 Estimating ARMA Time Series Models;281
12.3.3;20.3 Quadratic Discrimination of ARMA Time Series Models;282
12.3.4;20.4 Goodness of Fit for ARMA Time Series Models;284
12.3.5;20.5 Outliers in ARMA Time Series Models;286
12.3.6;References;290
12.4;21 Generalized Linear Models Diagnostics for Binary Data using Divergence Measures;292
12.4.1;21.1 Introduction;292
12.4.2;21.2 Checking Goodness-of-fit;294
12.4.3;21.3 Simulation Study;296
12.4.4;21.4 Outlying Detection Procedures;298
12.4.5;References;301
13;Part VIII Applied Mathematics;303
13.1;22 Some Problems in Geometric Processing of Surfaces;304
13.1.1;22.1 Introduction;304
13.1.2;22.2 Mathematical Preliminaries;305
13.1.3;22.3 Helical Curves on Surfaces;307
13.1.4;22.4 Silhouette Curve on a Surface;310
13.1.5;22.5 Conclusions and Further Remarks;313
13.1.6;References;314
13.2;23 Generalized Inverse Computation Based on an Orthogonal Decomposition Methodology;316
13.2.1;23.1 Introduction;316
13.2.2;23.2 Generalized Inverse;317
13.2.3;23.3 The Algorithm to Obtain a Generalized Inverse;318
13.2.4;23.4 Generalized Inverse Updating Algorithm;320
13.2.5;23.5 Least Squares Estimation for Less than Full Rank Models;323
13.2.6;23.6 Conclusions;326
13.2.7;References;326
13.3;24 Single and Ensemble Fault Classifiers Based on Features Selected by Multi- Objective Genetic Algorithms;327
13.3.1;24.1 Introduction;327
13.3.2;24.2 Feature Selection for Pattern Classification;328
13.3.3;24.3 GA-based Feature Selection for Pattern Classification;330
13.3.4;24.4 Classification of Transients in the Feedwater System of a Boiling Water Reactor;332
13.3.5;24.5 The Ensemble Approach to Pattern Classification;333
13.3.6;24.6 Application to Multiple Fault Classification;336
13.3.7;24.7 Conclusions;337
13.3.8;References;338
13.4;25 Feasibility Conditions in Engineering Problems Involving a Parametric System of Linear Inequalities;340
13.4.1;25.1 Introduction;340
13.4.2;25.2 The Heat Transfer Problem;341
13.4.3;25.3 A Fracture Mechanical Problem;344
13.4.4;25.4 The Beam Problem;345
13.4.5;25.5 Conclusions;349
13.4.6;References;349
13.5;26 Forecasting Nonlinear Systems with Neural Networks via Anticipated Synchronization;350
13.5.1;26.1 Introduction;350
13.5.2;26.2 Anticipated Synchronization;351
13.5.3;26.3 Nonlinear Time Series Modeling with Neural Networks;354
13.5.4;26.4 Error Growth in Synchronized Chains;356
13.5.5;26.5 Conclusions;358
13.5.6;References;358
14;Part IX Discrete Distributions;359
14.1;27 The Discrete Half-Normal Distribution;360
14.1.1;27.1 Introduction;360
14.1.2;27.2 The Maximum Entropy Derivation;361
14.1.3;27.3 The Limiting q-hyper-Poisson-I Derivation;362
14.1.4;27.4 The Morse M/M/1 Queue with Balking;362
14.1.5;27.5 Success Run Processes;363
14.1.6;27.6 Mixed Heine Distribution;364
14.1.7;27.7 Properties;365
14.1.8;References;366
14.2;28 Parameter Estimation for Certain q- Hypergeometric Distributions;368
14.2.1;28.1 Introduction;368
14.2.2;28.2 Special Cases and Properties;369
14.2.3;28.3 Estimation;371
14.2.4;References;372
15;Index;373