PROGRESS IN APPLIED STATISTICSRESEARCH

PROGRESS IN APPLIED STATISTICSRESEARCH

CONTENTS

PREFACE

Chapter 1AN APPROXIMATE FAST BAYESIAN ALGORITHMFOR THE ANALYSIS AND FORECASTING OF THELOGNORMAL TIME SERIES

Abstract

1. Introduction

2. The Standard Dynamic Linear Models

The observation equation

The state equation

3. Dynamic Generalized Linear Models

4. Conditional Independence Structure

5. Lognormal Dynamic Models

6. Validation

7. Conclusion

References

Chapter 2EFFICIENT UNIFORM DESIGNS FOR MIXTUREEXPERIMENTS IN THREE AND FOUR COMPONENTS∗

Abstract

1 Introduction

2 Uniform Designs and Uniformity Measures

3 Projection Designs

4 Optimality Criteria

5 Unconstrained Mixture Experiments

6 Constrained Mixture Experiments

Acknowledgments

Appendix A

References

Chapter 3DESIGN OF ACCELERATED LIFE TESTS FORPERIODIC INSPECTION WITH BURR TYPE IIIDISTRIBUTIONS: MODELS, ASSUMPTIONS ANDAPPLICATIONS

Abstract

1. Introduction

2. The Model and Test Method

Assumptions

Test Method

Standardization

3. Maximum Likelihood Estimation

4. Optimal Test Plans

Sensitivity Analysis

Sample Size Determination

5. Computational Results and Comparative Study

6. Test Procedure with Example

Example

7. Conclusion

References

Chapter 4PARAMETER ESTIMATION USING CRESSIE-READDIVERGENCE MEASURES WITH EXPONENTIALGROUPED CENSORED DATA∗

Abstract

1 Introduction

2 Computational Results

3 Findings and Conclusions

References

Chapter 5ESTIMATING THE VARIANCE COMPONENTSOF ACCELERATED DEGRADATION MODELS∗

Abstract

1 Introduction

2 Model and Estimating the Fixed Effect Parameters

3 Estimating the Variance Components

4 Simulation Study

5 Results and Conclusions

6 Application

References

Chapter 6ON THE RATIO OF THE SYMMETRIC DIFFERENCESOF ORDER STATISTICS

Abstract

1. Introduction

2. Main Result

References

Chapter 7MEASURING THE SURFACE ROUGHNESS USINGTHE SPATIAL STATISTICS APPLICATION

Abstract

1. Introduction and Notation

2. Spatial Statistics Analysis

3. Data Analysis

4. Conclusion

References

Chapter 8DIALLEL CROSSES WITH BLOCK SIZES THREE

Abstract

1. Introduction

2. Method of Construction

3. Analysis

4. Complete Diallel Crosses Plan with Unequal Number of Lines

4.1. Method of Construction

4.2. Analysis

5. Partial Diallel Crosses

6. Conclusion

Acknowledgements

Appendix: Tables

References

Chapter 9ON CHARACTERIZING DISTRIBUTIONS BYCONDITIONAL EXPECTATIONS OF FUNCTIONS OFGENERALIZED ORDER STATISTICS

Abstract

1. Introduction

2. Main Results

2.1. Applications

3. Characterizations by Reverse Ordering

3.1. Applications

Acknowledgments

References

Chapter 10ESTIMATING THE LOCATION AND SCALEPARAMETERS USING RANKED SET SAMPLING

Abstract

1. Introduction

2. Estimation Based on a RSS and a MRSS

3. Location Family

Scale Family

5. Location-Scale Family

6. Calculations

7. Application

8. Conclusion

References

Chapter 11ROBUST ESTIMATION IN CALIBRATIONMODELSUSING THE STUDENT-t DISTRIBUTION

Abstract

1. Introduction

2. The Calibration Model without Measurement Error

2.1. A Simulation Study

2.2. Application

3. The Functional Calibration Model

3.1. A Simulation Study

References

Chapter 12USEFUL RESULTS FOR THE RENEWALAND THE ALTERNATING RENEWAL PROCESS

Abstract

1. Introduction

2. Notation

3. The Mean Number of Excess Periods in [0, t).

4. The Alternating Renewal Process

5. A Correlated Alternating Renewal Process

6. The Mean Number of Periods in a Three State Renewal Process

7. A Correlated Three Stages Renewal Process

References

Chapter 13CLASSIFICATION OF MULTIVARIATEREPEATED MEASURES DATA WITHTEMPORAL AUTOCORRELATION

Abstract

1. Introduction

2. Classification Rules

2.1. Classification Rules with Structured Mean Vectors

Maximum Likelihood Estimation of d1,d2,V and S:

Classification Rule:

Classification Rule:

Classification Rule:

2.2. Classification Rules with Unstructured Mean Vectors

3. An Example

4. A Simulated Study

References

Chapter 14BAYESIAN ESTIMATION FOR THE AR(1) MODELUSING ASYMMETRIC LOSS FUNCTIONS

Abstract

1. Introduction

2. Linex Loss Functions

3. Rationale Behind the Asymmetric Loss

4. Different Prior Models

4.1. Conjugate Normal Prior and the Behavior of the Linex Risks

4.2. Alternatives to the Conjugate Prior

5. Decision Analysis

6. Data Analysis

References

Chapter 15BAYESIAN MODELLING FOR RECURRENTLIFETIME DATA WITH A NON HOMOGENEOUSPOISSON PROCESS WITH A FRAILTY TERM WITH AGAMMA OR INVERSE GAUSSIAN DISTRIBUTION

Abstract

1. Introduction

2. Model Formulation

2.1. The Model with a Gamma Frailty Distribution

2.2. The Model with an Inverse Gaussian Frailty Distribution

3. A Bayesian Approach

3.1. The Conditional Posterior for the Model with a Gamma Frailty Distribution

3.2. The Conditional Posterior for the Model with a Inverse Gaussian FrailtyDistribution

4. Model Selection

5. The Animal Carcinogenesis Data

6. Estimating the Individual Frailties

7. Concluding Remarks

Acknowledgments

References

Chapter 16LOCAL INFLUENCE FOR MEASUREMENT ERRORREGRESSION MODELS FOR THE ANALYSIS OFPRETEST/POSTTEST DATA

Abstract

1. Introduction

2. Measurement Error Regression Model with Null Intercept

3. Local Influence Diagnostics

3.1. Perturbation of CaseWeights

3.2. Perturbation of the Response Variables

3.3. Perturbation of the Explanatory Variables

3.4. Perturbation of the Variance of the Measurement Errors

4. Numerical Illustration

Appendix A: EM Algorithm

E Step

M Step

Appendix B: Observed Information Matrix

Acknowledgements

References

Chapter 17A TRANSITION MODEL FOR AN ORDEREDCLUSTER OF MIXED CONTINUOUS AND DISCRETERESPONSES WITH NON-MONOTONE MISSINGNESS

Abstract

1. Introduction

2. Psychological Disorders Data

3. Transition Model for Ordered Cluster or Longitudinal Datawith Non-monotone Missing Responses

3.1. Residuals

4. A Transition Model for the Psychological Disorders Data

4.1. The Model

4.2. Likelihood

4.3. Results

5. Discussion

Acknowledgment

References

Chapter 18ON A NONBINARY S-OPTIMAL DESIGN OVER ACLASS OF MINIMALLY CONNECTED BINARYROW-COLUMN DESIGNS

Abstract

1. Introduction

2. Preliminaries

3. s-optimal Minimal Design

4. Concluding Remarks

References

Chapter 19THE ERLANGIAN MACHINE INTERFERENCE MODEL:ER/M/2/K/N WITH BALKING, RENEGING ANDHETEROGENEOUS REPAIRMEN∗

Abstract

1. Introduction

2. Analyzing the Problem

3. The Steady−State Equations and Their Solution

4. Special Cases

References

Chapter 20SOME EXTENSIONS TO DOUBLERANKED SET SAMPLING∗

Abstract

1. Introduction

2. Sampling Methods

2.1. Ranked Set Sampling

2.2. Median Ranked Set Sampling

2.3. Extreme Ranked Set Sampling

2.4. Double Ranked Set Sampling

2.5. Median Double Ranked Set Sampling

2.6. Double Median Ranked Set Sampling

2.7. Extreme Double Ranked Set Sampling

3. Notations and Some Definitions

4. Median Double Ranked Set Sampling

4.1. Efficiency of MDRSS

4.2. Examples

5. Double Median Ranked Set Sampling

5.1. Efficiency of DMRSS

5.2. Examples

6. Extreme Double Ranked Set Sampling

6.1. Efficiency of EDRSS

6.2. Examples

7. Results and Discussion

Appendix

References

INDEX

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