search for books and compare prices
Tables of Contents for Probability and Statistical Models With Applications
Chapter/Section Title
Page #
Page Count
Preface
v
List of Contributors
xix
List of Tables
xxv
List of Figures
xxvii
Theophilos N. Cacoullos - A View of his Career
xxxix
Publications of Theophilos N. Cacoullos
xxxii
The Ten Commandments for a Statistician
xxxviii
Part I. Approximation, Bounds, and Inequalities
Nonuniform Bounds in Probability Approximations Using Stein's Method
3
12
Louis H. Y. Chen
Introduction
3
1
Poisson Approximation
4
3
Binomial Approximation: Binary Expansion of a Random Integer
7
2
Normal Approximation
9
2
Conclusion
11
4
References
11
4
Probability Inequalities for Multivariate Distributions with Applications to Statistics
15
26
Joseph Glaz
Introduction and Summary
15
2
Positive Dependence and Product-Type Inequalities
17
5
Negative Dependence and Product-Type Inequalities
22
1
Bonferroni-Type Inequalities
23
4
Applications
27
14
Sequential Analysis
27
1
A Discrete Scan Statistic
28
2
An Approximation for a Multinomial Distribution
30
1
A Conditional Discrete Scan Statistic
31
4
Simultaneous Prediction in Time Series Models
35
2
References
37
4
Applications of Compound Poisson Approximation
41
22
A. D. Barbour
O. Chryssaphinou
E. Vaggelatou
Introduction
41
4
First Applications
45
5
Runs
45
3
Sequence Matching
48
2
Word Counts
50
8
Discussion and Numerical Examples
58
5
References
60
3
Compound Poisson Approximation for Sums of Dependent Random Variables
63
24
Michael V. Boutsikas
Markos V. Koutras
Introduction
63
3
Preliminaries and Notations
66
1
Main Results
67
9
Examples of Applications
76
11
A Compound Poisson Approximation for Truncated Moving Sum of i.i.d. r.v.s
76
4
The Number of Overlapping Success Runs in a Stationary Two-State Markov Chain
80
5
References
85
2
Unified Variance Bounds and a Stein-Type Identity
87
14
N. Papadatos
V. Papathanasiou
Introduction
87
2
Properties of the Transformation
89
5
Application to Variance Bounds
94
7
References
98
3
Probability Inequalities for U-Statistics
101
16
Tasos C. Christofides
Introduction
101
2
Preliminaries
103
3
Probability Inequalities
106
11
References
112
5
Part II. Probability and Stochastic Processes
Theory and Applications of Decoupling
117
30
Victor de la Pena
T. L. Lai
Complete Decoupling of Marginal Laws and One-Sided Bounds
118
5
Tangent Sequences and Conditionally Independent Variables
123
1
Basic Decoupling Inequalities for Tangent Sequences
124
4
Applications to Martingale Inequalities and Exponential Tail Probability Bounds
128
2
Decoupling of Multilinear Forms, U-Statistics and U-Processes
130
4
Total Decoupling of Stopping Times
134
5
Principle of Conditioning in Weak Convergence
139
2
Conclusion
141
6
References
142
5
A Note on the Probability of Rapid Extinction of Alleles in a Wright-Fisher Process
147
8
F. Papangelou
Introduction
147
3
The Lower Bound for Boundary Sets
150
5
References
154
1
Stochastic Integral Functionals in an Asymptotic Split State Space
155
14
V. S. Korolyuk
N. Limnios
Introduction
155
1
Preliminaries
156
3
Phase Merging Scheme for Markov Jump Processes
159
1
Average of Stochastic Integral Functional
160
1
Diffusion Approximation of Stochastic Integral Functional
161
5
Single Splitting State Space
161
3
Double Split State Space
164
2
Integral Functional with Perturbed Kernel
166
3
References
167
2
Busy Periods for Some Queues with Deterministic Interarrival or Service Times
169
16
Claude Lefevre
Philippe Picard
Introduction
169
2
Preliminaries: A Basic Class of Polynomials
171
3
Construction of the Basic Polynomials
171
2
A Generalized Appell Structure
173
1
The Dg/M(Q)/1 Queue
174
5
Model and Notation
174
1
Exact Distribution of Nr
175
4
The M(Q)/Dg/1 Queue
179
6
Model and Notation
179
1
Exact Distribution of Nr
180
3
References
183
2
The Evolution of Population Structure of the Perturbed Non-Homogeneous Semi-Markov System
185
24
P.-C. G. Vassiliou
H. Tsakiridou
Introduction
185
2
The Perturbed Non-Homogeneous Semi-Markov System
187
3
The Expected Population Structure with Respect to the First Passage Time Probabilities
190
6
The Expected Population Structure with Respect to the Duration of a Membership in a State
196
3
The Expected Population Structure with Respect to the State Occupancy of a Membership
199
2
The Expected Population Structure with Respect to the Counting Transition Probabilities
201
8
References
203
6
Part III. Distributions, Characterizations, and Applications
Characterizations of Some Exponential Families Based on Survival Distributions and Moments
209
16
M. Albassam
C. R. Rao
D. N. Shanbhag
Introduction
209
2
An Auxiliary Lemma
211
1
Characterizations Based on Survival Distributions
212
6
Characterizations Based on Moments
218
7
References
222
3
Bivariate Distributions Compatible or Nearly Compatible with Given Conditional Information
225
14
B. C. Arnold
E. Castillo
J. M. Sarabia
Introduction
225
1
Imprecise Specification
226
2
Precise Specification
228
5
An Example
233
6
References
237
2
A Characterization of a Distribution Arising from Absorption Sampling
239
8
Adrienne W. Kemp
Introduction
239
3
The Characterization Theorem
242
2
An Application
244
3
References
245
2
Refinements of Inequalities for Symmetric Functions
247
6
Ingram Olkin
References
250
3
General Occupancy Distributions
253
16
Ch. A. Charalambides
Introduction
253
2
A General Random Occupancy Model
255
5
Special Occupancy Distributions
260
9
Geometric Probabilities
260
4
Bernoulli Probabilities
264
4
References
268
1
A Skew t Distribution
269
10
M. C. Jones
Introduction
269
1
Derivation of Skew t Density
270
2
Properties of Skew t Distribution
272
2
A First Bivariate Skew t Distribution
274
1
A Second Bivariate Skew t Distribution
275
4
References
277
2
On the Posterior Moments for Truncation Parameter Distributions and Identifiability by Posterior Mean for Exponential Distribution with Location Parameters
279
14
Y. Ma
N. Balakrishnan
Introduction
279
2
Posterior Moments
281
5
Examples
286
1
Identifiability by Posterior Mean
287
2
An Illustrative Example
289
4
References
289
4
Distributions of Random Volumes without Using Integral Geometry Techniques
293
26
A. M. Mathai
Introduction
294
5
Evaluation of Arbitrary Moments of the Random Volumes
299
20
Matrix-Variate Distributions for X
299
6
Type-1 Beta Distribution for X
305
2
The Case when the Rows of X are Independently Distributed
307
2
Type-1 Beta Distributed Independent Rows of X
309
1
Type-2 Beta Distributed Independent Rows of X
310
1
Independently Gaussian Distributed Points
311
1
Distributions of the r-Contents
312
4
References
316
3
Part IV. Time Series, Linear, and Non-Linear Models
Cointegration of Economic Time Series
319
14
T. W. Anderson
Introduction
319
1
Regression Models
320
1
Simultaneous Equation Models
321
2
Canonical Analysis and the Reduced Rank Regression Estimator
323
2
Autoregressive Processes
325
1
Nonstationary Models
326
1
Cointegrated Models
327
1
Asymptotic Distribution of Estimators and Test Criterion
328
5
References
331
2
On Some Power Properties of Goodness-of-Fit Tests in Time Series Analysis
333
16
Efstathios Paparoditis
Testing Spectral Density Fits
333
4
Local Power Considerations
337
3
Comparison
340
9
References
348
1
Linear Constraints on a Linear Model
349
10
Somesh Das Gupta
Introduction
349
2
Geometric Interpretation of the Role of the Linear Constraints
351
8
References
357
2
M-Methods in Generalized Nonlinear Models
359
20
Antonio I. Sanhueza
Pranab K. Sen
Introduction
359
2
Definitions and Assumptions
361
2
Asymptotic Results
363
8
Test of Significance and Computational Algorithm
371
8
Subhypothesis Testing
371
1
Nonlinear Hypothesis Testing
371
1
Computational Algorithm
372
1
References
373
6
Part V. Inference and Applications
Extensions of a Variation of the Isoperimetric Problem
379
12
Herman Chernoff
Introduction
379
1
Information Retrieval Problem
380
1
Information Retrieval without Measurement Error
381
1
Useful Information in a Variable
382
1
Allocation of Storage Space
383
1
The Isoperimetric Problem
383
1
Extensions
384
7
References
387
4
On Finding a Single Positive Unit in Group Testing
391
12
Milton Sobel
Introduction
391
1
Description of Properties, Numerical Results
392
4
Some Formulas for Procedure RDH
396
2
The Greedy Procedure RG
398
1
Conclusions
398
1
Changing the Prior with Procedure RDH
399
1
Robustness of Procedure RDH for q Known
400
3
References
401
2
Testing Hypotheses on Variances in the Presence of Correlations
403
16
A. M. Mathai
P. G. Moschopoulos
Bivariate Normal Population
403
3
Modifying the Hypothesis
406
2
Nonnull Moments
408
5
Null Case
413
2
The Conditional Hypothesis
415
4
References
418
1
Estimating the Smallest Scale Parameter: Universal Domination Results
419
10
Stavros Kourouklis
Introduction
419
1
Main Results
420
9
References
426
3
On Sensitivity of Exponential Rate of Convergence for the Maximum Likelihood Estimator
429
18
James C. Fu
Introduction
429
2
Main Results
431
5
Some Applications
436
6
Exponential Model
437
1
Families of t-distributions with Location Parameter
438
4
Discussion
442
5
References
443
4
A Closer Look at Weighted Likelihood in the Context of Mixtures
447
22
Marianthi Markatou
Introduction
447
2
Background
449
3
Simulation Experiments and Results
452
12
Normal Mixture with Equal Component Variance
454
4
Normal Mixtures with Unequal Component Variance
458
4
Other Models
462
2
Model Selection
464
1
Conclusions
465
4
References
465
4
On Nonparametric Function Estimation with Infinite-Order Flat-Top Kernels
469
16
Dimitris N. Politis
Introduction: A General Family of Flat-Top Kernels of Infinite Order
469
3
Multivariate Density Estimation: A Review
472
3
Further Issues on Density Estimation
475
10
Case of Smooth Density over a Finite Domain
476
2
Case of Infinite Domain with Some Discontinuities
478
3
References
481
4
Multipolishing Large Two-Way Tables
485
18
Kaye Basford
Stephan Morgenthaler
John W. Tukey
Introduction
485
1
Bilinear Multipolishers
486
3
Choosing the Auxiliary Variables Equal to the Effects of the Additive Fit
488
1
Robust Alternatives
489
1
Matrix Approximations
489
3
Approximations of Two-Way Tables
491
1
Displays
492
1
Example
493
2
Concluding Remarks
495
8
References
496
7
On Distances and Measures of Information: A Case of Diversity
503
14
Takis Papaioannou
Introduction
503
2
Measuring Information - Measures of Information
505
3
Properties of Measures of Information
508
1
Measures of Information and Inference
509
2
Applications
511
1
Conclusions
512
5
References
512
5
Representation Formulae for Probabilities of Correct Classification
517
20
Wolf-Dieter Richter
Introduction
517
2
Vector Algebraic Preliminaries
519
6
Distributional Results
525
12
Representation Formulae Based upon the Two-Dimensional Gaussian Law
525
6
Representation Formulae Based upon the Doubly Noncentral F-Distribution
531
3
References
534
3
Estimation of Cycling Effect on Reliability
537
12
Vilijandas Bagdonavicius
Mikhail Nikulin
Models
537
2
Semiparametric Estimation
539
10
The First Model
539
3
The Second Model
542
2
References
544
5
Part VI. Applications to Biology and Medicine
A New Test for Treatment vs. Control in an Ordered 2 X 3 Contingency Table
549
16
Arthur Cohen
H. B. Sackrowitz
Introduction
549
2
New Test, Implementation and Example
551
2
Simulation Study
553
1
Theoretical Properties
554
11
Appendix
559
4
References
563
2
An Experimental Study of the Occurrence Times of Rare Species
565
8
Marcel F. Neuts
Statement of the Problem
565
1
The Design of the Experiment
566
2
Stage 2 of the Experiment
568
1
Findings
569
4
References
571
2
A Distribution Functional Arising in Epidemic Control
573
10
Niels G. Becker
Sergey Utev
Introduction
573
1
Properties of the Functional
574
3
Proof of the Theorem
577
2
Application to Epidemic Control
579
4
References
581
2
Birth and Death Urn for Ternary Outcomes: Stochastic Processes Applied to Urn Models
583
18
A. Ivanova
N. Flournoy
Introduction
583
1
A Birth and Death Urn with Immigration for Ternary Outcomes
584
2
Embedding the Urn Scheme in a Continuous-Time Birth and Death Process
586
1
The Probability Generating Function for the Number of Success on Treatment i in the Continuous-Time Birth and Death Process
587
3
The Probability Generating Function for the Number of Trials on Treatment i in the Continuous-Time Birth and Death Process
590
1
The Number of Trials on Treatment i in the Continuous-Time Birth and Death Process
591
2
The Joint Probability Generating Function for the Number of Successes and the Number of Trials in the Continuous-Time Birth and Death Process
593
1
Adopting a Stopping Rule to Convert Continuous-Time Statistics to the Urn Design
594
2
Limiting Results for the Proportion of Trials on Treatment i
596
1
Limiting Results for the Proportion of Successes on Treatment i in the Urn
597
1
Asymptotic Inference Pertaining to the Success Probabilities
598
1
Concluding Remarks
599
2
References
600
1
Author Index
601
10
Subject Index
611