Kurume University Faculty of Economics Monograph Collection 18. Theoretical Advances and Applications in. Operations Research. Kyushu University Press

Transcription

1 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

2 Contents Preface i Chapter 1 Part I Stochastic Analysis Transmitting an Animal Infection to a Human Population Joe Gani and Randall J. Swift Introduction A Deterministic Model for Animal to Human Infection A Simple Stochastic Model for Fixed N Animal Infectives An Approximate Stochastic Model for Time Dependent Animal Infectives Concluding Remarks 15 Chapter 2 On the Mode of a Convolution Density Function of the Scaled Normal and Pearson Type VII Distributions Kangrong Tan Introduction Convolution Density Function of the Pearson Type VII and the Normal Distributions Convolution of the Pearson VII and the Normal Distributions Convolution of a Student t and a Normal Numerical Experiment Concluding Remarks 30

3 Chapter 3 Assessing Similarity of Two Survival Functions Based on Censored Data and the Trimmed Mallows Distance Yingchun Luo, Xianming Tan and Dongsheng Tu Introduction Definition of the Similarity of Survival Functions Based on the Trimmed Mallows Distance Empirical Trimmed Mallows Distance and Its Asymptotic Distribution Bootstrap Tests for Similarity Hypotheses Simulation Studies and Application to Data from a Clinical Trial Conclusions and Discussion 42 Chapter 4 Modeling Non-normal Phenomena Using a Mixture Distribution Kangrong Tan Introduction Properties of a Mixture Distribution Methodology of Mixture Distributions Some Properties of Mixture Distributions Generating Random Numbers Based upon a Mixture Distribution Estimation of Parameters and Weights Monte Carlo Simulation Based on Mixture Distributions Evaluating the VaR Particle Filtering with Non-normal Noise Approximation of Returns Distribution Based on the Mixture Distributions, Conventional Distributions Numerical Results Conclusions 69 Chapter 5 Analysis of the Tail Distribution of Network Link Delays Using Importance Sampling.. Kangrong Tan and Shozo Tokinaga Introduction Network Tomography and Its Estimation Network Tomography and Link Delay 75

4 5.2.2 Pseudo Likelihood Estimation The PLE Algorithm Network Topology Estimation Based on the GP Importance Sampling for Tail Distributions Rare Events and Importance Sampling Determining the Importance Function Numerical Applications Estimation for Artificially Generated Delays Improved Estimation by IS Other Network and Delay Distributions Delays with the Erlang Distribution Concluding Remarks 86 Chapter 6 Approximating a PDF with a Mixture Distribution and Its Application to Tail Distribution Analysis Kangrong Tan and Shozo Tokinaga Introduction Approximation of the p.d.f. Using the GA Why Use a Mixture Distribution? GA-based Optimization Analysis of Tail Distribution Improved Tail Estimation by IS Basics of IS Importance Function Numerical Experiments Stock Returns Tail Estimation Using IS Conclusion 106

5 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 Introduction Order Statistics Comparison of Statistical Properties of Returns and Ranges Descriptive Statistics Comparison of ACFs Fractality in Stock Ranges Applying Fractality to Estimate the Status of a Firm Kernel-based Discriminant Analysis Numerical Applications Concluding Remarks 125 Chapter 8 Distribution Approximation Based on the Tsallis Diffusion Process Kangrong Tan and Shozo Tokinaga Introduction The Tsallis Anomalous Diffusion Process Tsallis Entropy and the Fokker-Planck Equation GA-based Parameter Optimization Applications to Stock Markets Evolution of Daily and Intradaily Returns Evolution of Distributions over Time Spans 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 Introduction Summary of PF State Estimation and GP-based Approximation Estimation of True States Based upon Observed Data Basics of the PF 146

6 9.2.3 GP-based Equation Approximation Basic Functions Used for Approximation Model Setting and Suppression of Fluctuations Model W and Its State Estimation Numerical Results State Estimation and Supression for Artificial Data Application to Real Market Data Concluding Remarks. 155 Chapter 10 Bond Rating Based on Fuzzy Inference with Membership Functions Tuned by the Genetic Algorithm Kangrong Tan and Shozo Tokinaga Introduction Fuzzy Inference Optimization of Weight Discretization of Inference Result GA-based Membership Function Optimization Bond Rating Based on Fuzzy Inference Bond Rating Selection of Financial Ratios Discretizing the Bond Rating Categories Numerical Results Case I (exclusive data) Case II (partly using same data) Comparison with Other Methods Conclusion 175 Chapter 11 The State of the Art of Simulation Approaches Kangrong Tan and Shozo Tokinaga Introduction Simulation Approaches Monte Carlo Methods Quasi-Monte Carlo Methods Artificial Intelligence Methods 182

7 11.3 The MCMC Method Bayesian Inference Simulation Software Released Software Packages Building Programs Restrictions on Software and Hardware Some Solutions to the Restrictions 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 Introduction Continuous-time First Order Markov Processes with Nonnegative Integer Margins Based on Expectation Thinning The Heuristic SDE and Resulting Continuous-time First Order Markov Processes Independent Increment Processes The Generalized Ornstein-Uhlenbeck SDE Heuristic Solution to the Generalized SDE Some Resulting Cases Working Tool to Develop Models for Count Data Time Series Discussion 225 Index 229