发帖
雷达卡
Title:
Advances in Distribution Theory, Order Statistics, and Inference
N. Balakrishnan
Enrique Castillo
Jose Maria Sarabia
Editors
Size: 21.1MB(Only the download URL is provided)
Format: PDF
Content:
Preface xix
Barry C. Arnold: Career and Accomplishments xxi
Publications xxiii
Contributors xli
List of Tables xlvii
List of Figures li
PART I: DISCRETE DISTRIBUTIONS AND APPLICATIONS
1 Stochastic Comparisons of Bernoulli Sums and
Binomial Random Variables 3
P, J, Boland and H. Singh
1.1 Introduction 3
1.2 Stochastic Orders for Random Variables 5
1.3 Stochastic Order Comparisons for Sums of
Bernoulh Random Variables 6
1.4 Graphical Insight for Two-Dimensional Stochastic
Comparisons 8
References 11
2 Stopped Compound Poisson Process and
Related Distributions 13
C. Lefevre
2.1 Introduction 13
2.2 The Boundary Is Linear 15
2.3 The Boundary Is of Renewal Type 18
2.4 The Boundary Is Any Deterministic Function 19
2.5 A Higher Deterministic Boundary 22
References 25
vn
viii Contents
3 Constructions of Discrete Bivariate Distributions 29
C. D. Lai
3.1 Introduction 29
3.2 Mixing and Compounding 30
3.2.1 Mixing 30
3.2.2 Compounding 31
3.3 Trivariate Reduction 32
3.4 One Conditional and One Marginal Given 33
3.5 Conditionally Specified Method 34
3.6 Construction of Discrete Bivarite Distributions with
Given Marginals and Correlation 35
3.6.1 Discrete Frechet bounds 35
3.6.2 Probability functions of Frechet bounds 35
3.6.3 Construction of bivariate distributions 36
3.6.4 Construction of bivariate Poisson distributions 37
3.7 Sums and Limits of Bernoulli Trials 38
3.7.1 The bivariate Bernoulli distribution 38
3.7.2 Construction of bivariate Bernoulli distributions 38
3.8 Sampling from Urn Models 38
3.9 Clustering (Bivariate Distributions of Order k) 40
3.9.1 Preliminary 40
3.9.2 Bivariate distributions of order k 40
3.10 Construction of Finite Bivariate Distributions via Extreme
Points of Convex Sets 41
3.10.1 Finding extreme points 43
3.11 Generalized Distributions 43
3.11.1 Generalized bivariate distributions 44
3.11.2 Generalized bivariate Poisson distributions 44
3.11.3 Generalized bivariate general binomial distributions 45
3.12 Canonical Correlation Coefficients and Semigroups 45
3.12.1 Diagonal expansion 45
3.12.2 Canonical correlation coefficients and positive
definite sequence 46
3.12.3 Moment sequence and canonical correlation coefficient 46
3.12.4 Constructions of bivariate distributions via
canonical sequences 46
3.13 Bivariate Distributions from Accident Models 47
3.13.1 The Poisson-Poisson, Poisson-binomial, and
Poisson-Bernoulli methods 47
3.13.2 Negative binomial-Poisson and negative
binomial-Bernoulli models 48
3.14 Bivariate Distributions Generated from Weight Functions 48
3.15 Marginal Transformation Method 48
Contents ix
3.16 Truncation Methods 49
3.17 Construction of Positively Dependent Discrete Bivariate
Distributions 50
3.17.1 Positive quadrant dependent distributions 50
3.17.2 Positive regression dependent distributions 51
References 51
PART II: CONTINUOUS DISTRIBUTIONS AND APPLICATIONS
4 The Normal-Laplace Distribution and Its Relatives 61
W, J. Reed
4.1 Introduction 61
4.2 The Normal-Laplace Distribution 63
4.3 Related Distributions 68
4.3.1 The double Pareto-lognormal distribution 68
4.3.2 The generalized normal-Laplace distribution 68
4.4 A Levy Motion Based on the GNL Distribution 70
4.4.1 Option pricing for assets with logarithmic prices
following Brownian-Laplace motion 70
4.5 Estimation for ML and GNL Distributions 73
References 73
5 Some Observations on a Simple Means of Generating
Skew Distributions 75
A. Pewsey
5.1 Introduction 75
5.2 Flexibility and Limitations of the Construct 76
5.3 Inference 79
5.3.1 General considerations 79
5.3.2 Score equations for any Sfd^, ^, A) class 80
5.3.3 Observed information matrix for any Sfci^^ ^5 A) class 81
References 83
6 Bivariate Distributions Based on the Generalized
Three-Parameter Beta Distribution 85
J. M. Sarabia and E. Castillo
6.1 Introduction 85
6.2 The Generalized Three-parameter Best Distribution 87
6.2.1 Relationships with other distributions and extensions 88
6.3 Models with Generalized Three-Parameter Beta Marginals 89
6.3.1 Model based on the Dirichlet distribution 90
6.3.2 Model based on the Sarmanov-Lee distribution 91
Contents
6.4 The Generalized Three-Parameter Beta Conditionals
Distribution 92
6.4.1 The generalized beta conditionals distribution with
Xi{') constant 93
6.4.2 The generalized beta conditionals distribution with
constant a^(-) and bi{-) 97
6.4.3 Dependence conditions 100
6.5 Bivariate Distributions with with Gauss Hypergeometric
Conditionals 102
6.5.1 A flexible model 103
6.6 Other Bivariate Distributions with Specified
Conditionals 104
6.7 Applications to Bayesian Inference 105
6.8 Conditional Survival Models 106
6.9 Multivariate Extensions 107
References 108
7 A Kotz-Type Distribution for Multivariate
Statistical Inference 111
D. N. Naik and K. Plungpongpun
7.1 Introduction 111
7.1.1 Moments and other properties 113
7.1.2 Marginal and conditional distributions 114
7.2 An Algorithm for Simulation 114
7.3 Estimation of Parameters 117
7.3.1 Generalized spatial median (GSM) 118
7.3.2 Computation of GSM and E 118
7.3.3 The asymptotic distribution of GSM 119
7.4 An Example 121
References 122
8 Range of Correlation Matrices for Dependent
Random Variables with Given Marginal Distributions 125
H. Joe
8.1 Introduction 125
8.2 Known Results on a Range of Correlations 127
8.3 Conditional Approach 128
8.3.1 Multivariate normal and partial correlations 128
8.3.2 General case 130
8.4 Characterization of F for Sd{F) = S^ 132
8.4.1 d = 3 133
8.4.2 d > 3 136
8.5 Discussion 141
References 141
Contents xi
9 Multifractional Probabilistic Laws 143
M. D, Ruiz-Medina and J. M. Angulo
9.1 Introduction 143
9.2 Preliminaries 144
9.3 Fractional Differential Characterization 147
9.4 Multifractional Versions 148
9.5 Fractional and Multifractional Moment Laws 150
9.5.1 Multifracitonal moment laws 151
9.6 Conclusion 152
References 152
PART III: ORDER STATISTICS AND APPLICATIONS
10 Topics in the History of Order Statistics 157
H. A. David
10.1 Introduction 157
10.2 Early Measures of Location 158
10.3 Distribution Theory 162
10.4 Extreme-Value Theory 163
10.5 Estimation of Location and Scale Parameters by Linear
Functions of Order Statistics 166
10.6 Tables 167
References 168
11 Order Statistics from Independent Exponential
Random Variables and the Sum of the Top
Order Statistics 173
H. N. Nagaraja
11.1 Introduction 173
11.2 Distributional Representation and Basic Applications 174
11.2.1 Remarks 175
11.2.2 Applications 176
11.3 Sum of the Top Order Statistics 178
11.3.1 The IID case 179
11.3.2 The non-IID case 180
11.3.3 The IID case vs. the INID case 183
References 184
xii Contents
12 Fisher Information and Tukey's Linear Sensitivity
Measure Based on Ordered Ranked Set Samples 187
N. Balakrishnan and T. Li
12.1 Introduction 188
12.2 Maximum Likelihood Estimation Based on the ORSS 189
12.2.1 Logistic distribution 194
12.2.2 Normal distribution 195
12.2.3 One-parameter exponential distribution 196
12.2.4 Conclusions 197
12.3 Tukey's Linear Sensitivity Measure Based on ORSS 198
Appendix 203
References 204
13 Information Measures for Pareto Distributions and
Order Statistics * 207
M. Asadij N. Ebrahimi, G. G. Hamedani, and E. S. Soofi
13.1 Introduction 207
13.2 Information Measures 208
13.2.1 Shannon entropy 209
13.2.2 Renyi information measures 210
13.2.3 Dynamic information 210
13.2.4 Maximum entropy and maximum
dynamic entropy 212
13.3 Information Properties of Pareto Distributions 213
13.3.1 Characterizations of generalized Pareto 214
13.3.2 ME, MED, and MDEa characterizations
of Pareto 217
13.4 Information Properties of Order Statistics 217
References 221
14 Confidence Coefficients of Interpolated Nonpcirametric
Sign Intervals for Medians Under No or Weak Shape
Assumptions 225
0. Guilbaud
14.1 Introduction 225
14.2 Confidence Coefficient Under No Shape Assumption 227
14.3 Confidence Coefficient Under Symmetry 228
14.4 Confidence Coefficient Under Symmetry and
Unimodality 229
14.5 Domination Relations Among Interval Estimators 230
14.6 Nondominated Interval Estimators and Available
Confidence Coefficients 231
Contents xiii
14.7 Concluding Comments and Additional Results 233
Appendices 234
References 237
15 Small Sample Asymptotics for Higher-Order Spacings 239
R. Gatto and S. R. Jammalamadaka
15.1 Introduction 239
15.2 Tests Based on Higher-Order Spacings 241
15.3 Tests Based on Higher-Order Spacing-Frequencies 245
15.4 Conclusion 250
References 250
16 Best Bounds on Expectations of L-Statistics from
Bounded Samples 253
T. Rychlik
16.1 Introduction 253
16.2 General Results 254
16.3 Special Cases 259
References 262
PART IV: RELIABILITY AND APPLICATIONS
17 The Failure Rates of Mixtures 267
H. W. Block
17.1 Introduction 267
17.2 Notation 268
17.3 Examples 269
17.4 Asymptotics 270
17.5 Mixtures of Distributions with Linear Failure Rates 271
17.6 Mixtures of Standard Reliability Distributions 272
17.7 Preservation Under Mixtures 273
17.8 Analytic Tools for Determining the Shape of Mixtures 273
17.9 Coherent Systems 274
17.10 Summary of Overall Shape 275
References 275
18 Characterizations of the Relative Behavior of
Two Systems via Properties of Their Signature
Vectors 279
H. Block J M. R. Dugas, and F, J. Samaniego
18.1 Introduction 279
18.2 Background Results for the Comparison of
System Life 281
xiv Contents
18.3 New Signature Conditions and Associated
System Behavior 284
18.4 Practical Implications 286
References 289
19 Systems with Exchangeable Components and
Gumbel Exponential Distribution 291
J. Navarro, J. M. Ruiz, and C. J. Sandoval
19.1 Introduction 291
19.2 General Properties 292
19.3 Reliability and Moments 294
19.4 Aging Measures 298
19.5 Stochastic Orders and Classes 299
19.6 Parameter Estimation 302
19.7 Systems with n Exchangeable Components 303
References 305
20 Estimating the Mean of Exponential Distribution
from Step-Stress Life Test Data 307
Z. Chen, J, Mi, and Y. Y. Zhou
20.1 Introduction 307
20.2 Type I Censored Data 309
20.3 Grouped Data 314
20.4 Type II Censored Data 317
20.5 Simulation Study 324
References 325
21 Random Stress-Dependent Strength Models Through
Exponential Conditionals Distributions 327
A. SenCupta
21.1 Introduction 327
21.2 Bivariate Exponential Conditionals Distribution 328
21.3 Properites of BCE 330
21.3.1 Dependency properties of BCE 331
21.4 Model Representations in ALT 332
21.5 Statistical Inference under Normal Stress 333
21.5.1 Estimation of a and (3 334
21.5.2 Asymptotic inference for OQ 335
21.6 Unconditional Reliability Function and Measure 336
21.7 Conclusions 337
References 338
Contents xv
PART V: INFERENCE
22 Some New Methods for Local Sensitivity Analysis
in Statistics 343
E. Castillo, C Castillo J A. S. Hadi, and J. M. Sarabia
22.1 Introduction and Motivation 343
22.2 Sensitivities of the Objective Function 344
22.3 AppHcations to Regression 346
22.3.1 Least-squares regression 346
22.3.2 Minimax regression 347
22.3.3 Mixed least-squares and minimax regression 348
22.3.4 Example: Simulated data 348
22.4 The Maximum Likelihood Function 350
22.4.1 Local sensitivites 351
22.4.2 Examples: The gamma and beta families 351
22.5 Ordered and Data Constrained Parameters 351
22.6 The Method of Moments Estimates 354
22.6.1 Local sensitivities 354
22.6.2 Example 1: The gamma family 355
22.6.3 Example 2: The beta family 356
22.7 Conclusions 358
References 359
23 t-Tests with Models Close to the Normal Distribution 363
A. Garcia-Perez
23.1 Introduction 363
23.2 Prehminaries 364
23.2.1 Influence functions of p ^ and fc^ 366
23.2.2 Von Mises expansions of p ^ and fc^ 367
23.2.3 Von Mises approximations of p ^ and fc^
with a model F close to the normal distribution 368
23.3 Von Mises Approximations for t-Tests 369
23.4 Saddlepoint Approximations for t-Tests 373
References 378
24 Computational Aspect of the Chi-Square Goodness-of-Fit
Test Applications 381
M. Divinsky
24.1 Introduction 381
24.2 On the Chi-Square Test Application 382
24.3 An Actual Data Set 383
24.4 Modeled Sample of the Generated Values 385
xvi Contents
24.5 Conclusions 386
References 387
25 An Objective Bayesian Procedure for Variable Selection
in Regression 389
F. J. Giron, E. Moreno, and M. L. Martinez
25.1 Introduction 389
25.2 Intrinsic Priors for Variable Selection 391
25.3 Bayes Factors and Model Posterior Probabilities 393
25.4 Relation with the R^ and Other Classical Criterior for
Model Selection 394
25.5 Examples 397
25.5.1 Simulation study 397
25.5.2 Raid's data 398
25.5.3 Prostate cancer data 399
25.6 Conclusions 401
References 402
26 On Bayesian and Decision-Theoretic Approaches to
Statistical Prediction 405
T. K. Nayak and A. El-Baz
26.1 Introduction 405
26.2 Bayesian Prediction 407
26.3 Admissible Predictors 410
References 414
27 Phi-Divergence-Type Test for Positive Dependence
Alternatives in 2 x /c Contingency Tables 417
L. Pardo and M. L. Menendez
27.1 Introduction 417
27.2 Phi-Divergence Test Statistics 419
27.3 Asymptotic Distribution of the (/^Divergence
Test Statistics 425
References 430
28 Dimension Reduction in Multivariate Time Series 433
D. Pena and P. Poncela
28.1 Introduction 433
28.2 Models for Dimension Reduction 435
28.2.1 Principal components 435
28.2.2 The Box and Tiao canonical analysis 436
28.2.3 Reduced rank models 438
Contents xvii
28.2.4 The scalar components models 439
28.2.5 Dynamic factor models 440
28.2.6 State space models 441
28.2.7 Some conclusions 442
28.3 Dimension Reduction Tests 443
28.3.1 A test for zero canonical correlation
coefficients 443
28.3.2 A nonstandard test for canonical
correlations 445
28.3.3 A canonical correlation test for factor
models 448
28.4 Real Data Analysis 449
28.5 Concluding Remarks 455
References 456
29 The Hat Problem and Some Variations 459
W. GuOj S. Kasala, M. B, Rao, and B. Tucker
29.1 Introduction 459
29.2 Hamming Codes 461
29.3 Three Team Mates and Three Colors 464
29.4 Three Team Mates and m Colors 466
29.5 An Upper Bound for the Winning Probability 468
29.6 General Distribution 471
29.7 Other Variations 478
29.8 Some Open Problems 478
29.9 The Yeast Genome Problem 478
References 479
Index 481
[此贴子已经被作者于2009-3-20 8:34:34编辑过]
提升卡
置顶卡
沉默卡
变色卡
抢沙发
千斤顶
显身卡
京公网安备 11010802022788号
