Kurume University Faculty of Economics Monograph Collection 18 Theoretical Advances and Applications in Operations Research Managing Editor Kangrong Tan General Advisor Joe Gani Kyushu University Press
Contents Preface i Chapter 1 Part I Stochastic Analysis Transmitting an Animal Infection to a Human Population Joe Gani and Randall J. Swift 3 1.1 Introduction 4 1.2 A Deterministic Model for Animal to Human Infection 4 1.3 A Simple Stochastic Model for Fixed N Animal Infectives 10 1.4 An Approximate Stochastic Model for Time Dependent Animal Infectives 13 1.5 Concluding Remarks 15 Chapter 2 On the Mode of a Convolution Density Function of the Scaled Normal and Pearson Type VII Distributions Kangrong Tan 17 2.1 Introduction 18 2.2 Convolution Density Function of the Pearson Type VII and the Normal Distributions 18 2.2.1 Convolution of the Pearson VII and the Normal Distributions 19 2.2.2 Convolution of a Student t and a Normal 24 2.3 Numerical Experiment 25 2.4 Concluding Remarks 30
Chapter 3 Assessing Similarity of Two Survival Functions Based on Censored Data and the Trimmed Mallows Distance Yingchun Luo, Xianming Tan and Dongsheng Tu 33 3.1 Introduction 34 3.2 Definition of the Similarity of Survival Functions Based on the Trimmed Mallows Distance 35 3.3 Empirical Trimmed Mallows Distance and Its Asymptotic Distribution 36 3.4 Bootstrap Tests for Similarity Hypotheses 38 3.5 Simulation Studies and Application to Data from a Clinical Trial.. 40 3.6 Conclusions and Discussion 42 Chapter 4 Modeling Non-normal Phenomena Using a Mixture Distribution Kangrong Tan 47 4.1 Introduction 48 4.2 Properties of a Mixture Distribution 49 4.2.1 Methodology of Mixture Distributions 49 4.2.2 Some Properties of Mixture Distributions 51-4.2.3 Generating Random Numbers Based upon a Mixture Distribution 55 4.2.4 Estimation of Parameters and Weights 57 4.3 Monte Carlo Simulation Based on Mixture Distributions 59 4.3.1 Evaluating the VaR 59 4.3.2 Particle Filtering with Non-normal Noise 60 4.4 Approximation of Returns Distribution Based on the Mixture Distributions, 64 4.4.1 Conventional Distributions 64 4.4.2 Numerical Results 66 4.5 Conclusions 69 Chapter 5 Analysis of the Tail Distribution of Network Link Delays Using Importance Sampling.. Kangrong Tan and Shozo Tokinaga 73 5.1 Introduction 74 5.2 Network Tomography and Its Estimation 75 5.2.1 Network Tomography and Link Delay 75
5.2.2 Pseudo Likelihood Estimation 77 5.2.3 The PLE Algorithm 77 5.3 Network Topology Estimation Based on the GP 78 5.4 Importance Sampling for Tail Distributions 80 5.4.1 Rare Events and Importance Sampling 80 5.4.2 Determining the Importance Function 81 5.5 Numerical Applications. 82 5.5.1 Estimation for Artificially Generated Delays 82 5.5.2 Improved Estimation by IS 83 5.5.3 Other Network and Delay Distributions 84 5.5.4 Delays with the Erlang Distribution 85 5.6 Concluding Remarks 86 Chapter 6 Approximating a PDF with a Mixture Distribution and Its Application to Tail Distribution Analysis Kangrong Tan and Shozo Tokinaga 89 6.1 Introduction 90 6.2 Approximation of the p.d.f. Using the GA 91 6.2.1 Why Use a Mixture Distribution? 91 6.2.2 GA-based Optimization 93 6.2.3 Analysis of Tail Distribution 94 6.3 Improved Tail Estimation by IS 95 6.3.1 Basics of IS 95 6.3.2 Importance Function 96 6.4 Numerical Experiments 100 6.4.1 Stock Returns 100 6.4.2 Tail Estimation Using IS 103 6.5 Conclusion 106
Part II Stochastic Analyses Combined with Artificial Intelligence Approaches in Recent Operations Research Chapter 7 Estimating Firm Status Based on the Statistical Properties of Stock Ranges.. Kangrong Tan and Shozo Tokinaga 111 7.1 Introduction 112 7.2 Order Statistics 113 7.3 Comparison of Statistical Properties of Returns and Ranges... 115 7.3.1 Descriptive Statistics 116 7.3.2 Comparison of ACFs 117 7.3.3 Fractality in Stock Ranges 118 7.4 Applying Fractality to Estimate the Status of a Firm 122 7.4.1 Kernel-based Discriminant Analysis 122 7.4.2 Numerical Applications 123 7.5 Concluding Remarks 125 Chapter 8 Distribution Approximation Based on the Tsallis Diffusion Process Kangrong Tan and Shozo Tokinaga 127 8.1 Introduction 128 8.2 The Tsallis Anomalous Diffusion Process 129 8.2.1 Tsallis Entropy and the Fokker-Planck Equation 129 8.2.2 GA-based Parameter Optimization 131 8.3 Applications to Stock Markets 133 8.3.1 Evolution of Daily and Intradaily Returns 133 8.3.2 Evolution of Distributions over Time Spans 134 8.4 Concluding Remarks 139 Chapter 9 Suppression of Fluctuations in Predictions of Particle Filtering with the State Equation Approximated by Genetic Programming Shozo Tokinaga and Kangrong Tan 143 9.1 Introduction 144 9.2 Summary of PF State Estimation and GP-based Approximation.. 145 9.2.1 Estimation of True States Based upon Observed Data... 145 9.2.2 Basics of the PF 146
9.2.3 GP-based Equation Approximation 147 9.2.4 Basic Functions Used for Approximation 147 9.3 Model Setting and Suppression of Fluctuations 148 9.3.1 Model W and Its State Estimation 148 9.4 Numerical Results 150 9.4.1 State Estimation and Supression for Artificial Data 150 9.4.2 Application to Real Market Data 152 9.5 Concluding Remarks. 155 Chapter 10 Bond Rating Based on Fuzzy Inference with Membership Functions Tuned by the Genetic Algorithm Kangrong Tan and Shozo Tokinaga 159 10.1 Introduction 160 10.2 Fuzzy Inference 161 10.2.1 Optimization of Weight 161 10.2.2 Discretization of Inference Result 162 10.2.3 GA-based Membership Function Optimization 163 10.3 Bond Rating Based on Fuzzy Inference 166 10.3.1 Bond Rating 166 10.3.2 Selection of Financial Ratios 167 10.3.3 Discretizing the Bond Rating Categories 169 10.4 Numerical Results 170 10.4.1 Case I (exclusive data) 170 10.4.2 Case II (partly using same data) 172 10.4.3 Comparison with Other Methods 172 10.5 Conclusion 175 Chapter 11 The State of the Art of Simulation Approaches Kangrong Tan and Shozo Tokinaga 177 11.1 Introduction 178 11.2 Simulation Approaches 178 11.2.1 Monte Carlo Methods 179 11.2.2 Quasi-Monte Carlo Methods 181 11.2.3 Artificial Intelligence Methods 182
11.3 The MCMC Method 183 11.3.1 Bayesian Inference 183 11.4 Simulation Software 190 11.4.1 Released Software Packages 191 11.4.2 Building Programs 192 11.4.3 Restrictions on Software and Hardware 193 11.4.4 Some Solutions to the Restrictions 193 11.5 Summary." 194 Chapter 12 A Heuristic Type of SDEs and the Resulting Class of Continuous-time First Order Markov Processes with Non-negative Integer-valued Margins Rong Zhu 197 12.1 Introduction 198 12.2 Continuous-time First Order Markov Processes with Nonnegative Integer Margins Based on Expectation Thinning 201 12.3 The Heuristic SDE and Resulting Continuous-time First Order Markov Processes 206 12.3.1 Independent Increment Processes 207 12.3.2 The Generalized Ornstein-Uhlenbeck SDE 208 12.3.3 Heuristic Solution to the Generalized SDE 210 12.3.4 Some Resulting Cases 216 12.3.5 Working Tool to Develop Models for Count Data Time Series 222 12.4 Discussion 225 Index 229