FOREWORD
PREFACE
LIST OF TABLES
LIST OF FIGURES

CHAPTER 1 - INTRODUCTION TO FREQUENCY ANALYSIS USING HALPHEN DISTRIBUTIONS

CHAPTER 2 - HALPHEN DISTRIBUTION FAMILY: MATHEMATICAL AND STATISTICAL PROPERTIES
2.1 - HISTORICAL CONTEXT
2.2 - HALPHEN DISTRIBUTION TYPE A (HA)
2.2.1 - Introduction
2.2.2 - Moments and Moment Ratios
2.2.3 - Sufficient Statistics
2.2.4 - Related Distributions
2.3 - HALPHEN DISTRIBUTION TYPE B (HB)
2.3.1 - Introduction
2.3.2 - Moments and Moment Ratios
2.3.3 - Sufficient Statistics
2.3.4 - Related Distribution
2.4 - HALPHEN DISTRIBUTION TYPE INVERSE B (HIB)
2.4.1 - Introduction
2.4.2 - Moments and Moment Ratios
2.4.3 - Sufficient Statistics
2.4.4 - Related Distribution
2.5 - SUMMARY

CHAPTER 3 - ASYMPTOTIC BEHAVIOR OF THE HALPHEN DISTRIBUTIONS
3.1. - INTRODUCTION
3.2. - CLASSES OF HEAVY TAILED DISTRIBUTIONS AND EXTREME VALUE THEORY
3.3. - ASYMPTOTIC BEHAVIOR AND DECISION SUPPORT SYSTEM
3.3.1. - Asymptotic Behavior
3.3.2. - Asymptotic Behavior for the Halphen Distributions
3.3.3. - Decision Support System
3.4. - THE HALPHEN FAMILY AND THE GENERALIZED EXTREME VALUE (GEV) SYSTEM, A COMPARISON
3.4.1. - Introduction
3.4.2. - Theoretical Arguments
3.5. - TESTING HA AND HB AGAINST THE GAMMA DISTRIBUTION
3.5.1. - Hypothesis and Alternatives
3.5.2. - Moment Ratio Diagram: Test Elaboration
3.5.3. - Power Study
3.5.4. - Conclusion

CHAPTER 4 - PARAMETER ESTIMATION METHODS FOR THE HALPHEN DISTRIBUTIONS
4.1. - INTRODUCTION
4.2. - MAXIMUM LIKELIHOOD METHOD (ML)
4.2.1. - ML for the HA Distribution
4.2.2. - ML for the HB Distribution
4.2.3. - ML for the HIB Distribution
4.3. - THE METHOD OF MOMENT (MM)
4.3.1. - MM for HA Distribution
4.3.2. - MM for HB Distribution
4.3.3. - MM for HIB Distribution
4.4. - The ITERATIVE MIXED METHOD (IMM)
4.5. - The BAYESIAN APPROACH FOR HALPHEN DISTRIBUTIONS
4.6. - CONCLUSION

CHAPTER 5 - MONTE CARLO SIMULATIONS FOR HALPHEN DISTRIBUTIONS
5.1. - INTRODUCTION
5.2. - MONTE CARLO SIMULATION AND RANDOM VARIABLE GENERATION
5.3. - THE ACCEPTATION-REJECTION APPROACH FOR THE HALPHEN DISTRIBUTIONS
5.3.1. - The Acceptance-Rejection Method (A-R)
5.3.2. - Halphen Type A Distribution (HA)
5.3.3. - Halphen Type B Distribution (HB)
5.3.4. - Halphen Type IB Distribution (HIB)
5.4. - MARKOV CHAIN MONTE CARLO METHOD (MCMC)
5.5. - CONCLUSION

CHAPTER 6 - MATLAB CODES FOR HALPHEN FITTING AND GENERATING (HFG)
6.1. - INTRODUCTION
6.2. - DSS CODE
6.3. - GENERATION OF HALPHEN DISTRIBUTIONS
6.4. - ESTIMATION OF THE PARAMETERS OF THE HALPHEN DISTRIBUTIONS
6.5. - QUANTILE FUNCTIONS
6.6. - CASE STUDY
6.7. - CONCLUSION

APPENDIX A: BESSEL FUNCTIONS
A.1. - Recursive relations
A.2. - Asymptotic properties
A.3. - Dispersion function
APPENDIX B: EXPONENTIAL FACTORIAL FUNCTION
B.1. - Recurrence relations
B.2. - Asymptotic relations
B.3. - Dispersion function

APPENDIX C: DECISION SUPPORT SYSTEM
C.1. - Log-Log Plot
C.2. - The Mean Excess Function Diagram (MEF)
C.3. - Hill's Ratio Plot
C.4. - Jackson Statistic

APPENDIX D: BAYESIAN FRAMEWORK
References
Author Index
Subject Index
Abbreviations and Symbols (Citation Page)