Advances in Mathematical and Statistical Modeling (eBook)

Barry C. Arnold, N. Balakrishnan, Jose-Maria Sarabia Alegria, Roberto Minguez (Herausgeber)

eBook Download: PDF

2009 | 2008
XXXIV, 368 Seiten
Birkhäuser Boston (Verlag)
978-0-8176-4626-4 (ISBN)

Infos

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.

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Enrique Castillo is a leading figure in several mathematical and engineering fields, having contributed seminal work in such areas as statistical modeling, extreme value analysis, multivariate distribution theory, Bayesian networks, neural networks, functional equations, artificial intelligence, linear algebra, optimization methods, numerical methods, reliability engineering, as well as sensitivity analysis and its applications. Organized to honor Castillo's significant contributions, this volume is an outgrowth of the "e;International Conference on Mathematical and Statistical Modeling,"e; 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. The book is divided into nine major sections, which include distribution theory and applications, probability and statistics, order statistics and analysis, engineering modeling, extreme value theory, business and economics applications, statistical methods, applied mathematics, and discrete distributions.This comprehensive reference work will appeal to a diverse audience from the statistical, applied mathematics, engineering, and economics communities. Practitioners, researchers, and graduate students in mathematical and statistical modeling, optimization, and computing will benefit from this work.

Inhalt

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 Castillo’s 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
12.5 Combining Two Independent Models 198
References 199
13 Ratio of Maximum to the Sum for Testing Super Heavy Tails 200
13.1 Introduction 200
13.2 Main Results 202
13.3 Simulation Results and Real Data Analysis 203
13.4 Auxiliary Results 207
13.5 Proofs 208
References 212
14 Tail Behaviour: An Empirical Study 214
14.1 Introduction 214
14.2 Asymptotic CI’s for the Tail Index and the VaR 216
14.3 Reduced Bias Tail Index and Quantile Estimators 217
14.4 An Algorithm for Semi-Parametric Tail Estimation 219
14.5 The Use of a Parametric Quantile Method in Tail Index and Quantile Estimation 220
14.6 Financial Data Analysis 222
References 225
15 An Example of Real–Life Data Where the Hill Estimator is Correct 227
15.1 Introduction 227
15.2 The Pareto Modeling 228
15.3 The Hill Estimator 229
15.4 Modified Pickands Estimators 230
15.5 Analyzing the Long Term Copepod Data 231
15.6 Computational Aspects 233
References 233
Part VI Business and Economics Applications 235
16 Deriving Credibility Premiums Under Different Bayesian Methodology 236
16.1 Introduction 236
16.2 Classical Model of Bühlmann 238
16.3 Standard Bayesian Credibility 239
16.4 Credibility Based on Robust Bayesian Analysis 240
16.5 Beyond the Loss Function 243
16.6 Discussion 245
References 245
17 The Influence of Transport Links on Disaggregation and Regionalization Methods in Interregional Input- Output Models Between Metropolitan and Remote Areas 247
17.1 Introduction 247
17.2 Methodology 248
17.3 Results and Discussion 252
17.4 Conclusions 256
References 256
Part VII Statistical Methods 258
18 Jackknife Bias Correction of a Clock Offset Estimator 259
18.1 Introduction 259
18.2 Candidate Clock Offset Estimators 261
18.3 Mean Squared Error Under Exponential and Pareto Distributions 262
18.4 Additional Mean Squared Error Comparisons via Simulation 264
18.5 Summary 267
References 268
19 Pretesting in Polytomous Logistic Regression Models Based on Phi- divergence Measures 269
19.1 Introduction 269
19.2 Preliminaries and Notation 271
19.3 Contiguous Alternative Hypotheses 273
19.4 Asymptotic Distributional Quadratic Risk of ßf2, ßH0f2 and ßpref1,f2 276
19.5 Comparison of ßf2, ßH0f2 and ßpref1,f2 278
References 279
20 A Unified Approach to Model Selection, Discrimination, Goodness of Fit and Outliers in Time Series 280
20.1 Introduction 280
20.2 Estimating ARMA Time Series Models 281
20.3 Quadratic Discrimination of ARMA Time Series Models 282
20.4 Goodness of Fit for ARMA Time Series Models 284
20.5 Outliers in ARMA Time Series Models 286
References 290
21 Generalized Linear Models Diagnostics for Binary Data using Divergence Measures 292
21.1 Introduction 292
21.2 Checking Goodness-of-fit 294
21.3 Simulation Study 296
21.4 Outlying Detection Procedures 298
References 301
Part VIII Applied Mathematics 303
22 Some Problems in Geometric Processing of Surfaces 304
22.1 Introduction 304
22.2 Mathematical Preliminaries 305
22.3 Helical Curves on Surfaces 307
22.4 Silhouette Curve on a Surface 310
22.5 Conclusions and Further Remarks 313
References 314
23 Generalized Inverse Computation Based on an Orthogonal Decomposition Methodology 316
23.1 Introduction 316
23.2 Generalized Inverse 317
23.3 The Algorithm to Obtain a Generalized Inverse 318
23.4 Generalized Inverse Updating Algorithm 320
23.5 Least Squares Estimation for Less than Full Rank Models 323
23.6 Conclusions 326
References 326
24 Single and Ensemble Fault Classifiers Based on Features Selected by Multi- Objective Genetic Algorithms 327
24.1 Introduction 327
24.2 Feature Selection for Pattern Classification 328
24.3 GA-based Feature Selection for Pattern Classification 330
24.4 Classification of Transients in the Feedwater System of a Boiling Water Reactor 332
24.5 The Ensemble Approach to Pattern Classification 333
24.6 Application to Multiple Fault Classification 336
24.7 Conclusions 337
References 338
25 Feasibility Conditions in Engineering Problems Involving a Parametric System of Linear Inequalities 340
25.1 Introduction 340
25.2 The Heat Transfer Problem 341
25.3 A Fracture Mechanical Problem 344
25.4 The Beam Problem 345
25.5 Conclusions 349
References 349
26 Forecasting Nonlinear Systems with Neural Networks via Anticipated Synchronization 350
26.1 Introduction 350
26.2 Anticipated Synchronization 351
26.3 Nonlinear Time Series Modeling with Neural Networks 354
26.4 Error Growth in Synchronized Chains 356
26.5 Conclusions 358
References 358
Part IX Discrete Distributions 359
27 The Discrete Half-Normal Distribution 360
27.1 Introduction 360
27.2 The Maximum Entropy Derivation 361
27.3 The Limiting q-hyper-Poisson-I Derivation 362
27.4 The Morse M/M/1 Queue with Balking 362
27.5 Success Run Processes 363
27.6 Mixed Heine Distribution 364
27.7 Properties 365
References 366
28 Parameter Estimation for Certain q- Hypergeometric Distributions 368
28.1 Introduction 368
28.2 Special Cases and Properties 369
28.3 Estimation 371
References 372
Index 373

Produkt-Details

• Erscheint lt. Verlag: 9.4.2009
• Reihe/Serie: Statistics for Industry and Technology
• Reihe/Serie: Statistics for Industry and Technology
• Zusatzinfo: XXXIV, 368 p. 56 illus.
• Verlagsort: Boston
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik
• Themenwelt: Wirtschaft
• Schlagworte: Artificial Intelligence • best fit • computing • distribution theory and order statistics • Estimator • extreme value theory • Factor Analysis • fatigue models • financial modeling • general inference • Generalized Linear Model • measure • modeling in business and economics • neural networks and computational techniques • Numerical Methods • Optimization • Optimization Methods • Pretest • quality control • Random Variable • Re • Regression • Statistics • Time Series
• ISBN-10: 0-8176-4626-4 / 0817646264
• ISBN-13: 978-0-8176-4626-4 / 9780817646264