| dc.description.tableofcontents | 謝辭\nABSTRACT\nContents\nFigures\nTables\nChapter 1 Introduction-----1\nChapter 2 Literature Review-----3\n 2.1 Stochastic Search Methods for Global Optimization-----3\n 2.2 Kennedy`s Algorithm-----4\n 2.3 The RAnge of Parameters-----8\nChapter 3 Tools for Use in Simulations-----10\n 3.1 Introduction-----10\n 3.2 RAndom Number Generator-----10\n 3.3 Chi-Square Goodness-of-Fit Test-----11\n 3.4 The Up-And-Down Test-----12\n 3.5 Flow Diagrams for the Simulation-----13\nChapter 4 Simulation Results-----17\n 4.1 Uniformity And RAndomness of the Congruential Generator-----17\n 4.2 The AcceptAnce Probability of the Goodness-of-Fit Test-----18\n 4.3 The "Best" Combination of k, p, q, r-----19\n 4.3.1 Symmetric Cases-----20\n 4.3.2 Right-Skewed Cases-----26\n 4.3.3 Left-Skewed Cases-----37\n 4.4 The Speed of Convergence-----44\nChapter 5 Conclusions-----48\nAppendix-----50\nReferences-----59\n\nFigures\nFigure 2.1 Diagram for choosing the first subinterval from [0,1].-----5\nFigure 3.5.1 Flow diagram for testing "randomness" and Uniform(0,1) of a random number generator.-----14\nFigure 3.5.2 Flow diagram for comparing all possible combinations of k, p, q, r which generate Beta(k(p+r),k(q+r)).-----15\nFigure 3.5.3 Flow diagram for calculating the mean frequencies T of the interval which converges with the final length < 0.001 for all possible combinations of k, p, q, r.-----16\nFigure 4.1 100 sample points are grouped into 10 categories where each category has length 0.1.-----18\nFigure 4.2 The acceptance probability of the test hypothesis H<sub>0</sub>：F(x) = Beta(4,4) distribution for different sample sizes given k = 5, p = 1/5, q =1/5, r =3/5.-----19\nFigure 4.3 The pdf of Beta(m,m) distribution.-----20\nFigure 4.4 The pdf of a Beta(m,n) distribution with m<n.-----26\nFigure 4.5.1 The probability that the goodness-of-fit test accepts vs k when a Beta(2,5) distribution is generated.-----27\nFigure 4.5.2 The probability that the goodness-of-fit test accepts vs k when a Beta(3,4) distribution is generated.-----27\nFigure 4.5.3 The probability that the goodness-of-fit test accepts vs k when a Beta(3,5) distribution is generated.-----27\nFigure 4.5.4 The probability that the goodness-of-fit test accepts vs k when a Beta(2,7) distribution is generated.-----27\nFigure 4.6 The pdf of a Beta(m,n) distribution with m>n.-----37\n\nTables\nTable 4.1 100 sample points generated by generator (4.1.1)-----17\nTable 4.2 The values of P(goodness-of-fit test accept ∣k, p, q, r) and standard deviations when a Beta(1,1) distribution is generated-----22\nTable 4.3 The values of P(goodness-of-fit test accept │k, p, q, r) and standard deviations when a Beta(2,2) distribution is generated-----22\nTable 4.4 The values of P(goodness-of-fit test accept │k, p, q, r) and standard deviations when a Beta(3,3) distribution is generated-----23\nTable 4.5 The values of P(goodness-of-fit test accept │k, p, q, r) and standard deviations when a Beta(4,4) distribution is generated-----24\nTable 4.6 The values of P(goodness-of-fit test accept │k, p, q, r) and standard deviations when a Beta(5,5) distribution is generated-----25\nTable 4.7 The values of P(goodness-of-fit test accept │k, p, q, r) and standard deviations when a Beta(2/3,5/3) distribution is generated-----28\nTable 4.8 The values of P(goodness-of-fit test accept │k, p, q, r) and standard deviations when a Beta(1.2) distribution is generated-----28\nTable 4.9 The values of P(goodness-of-fit test accept │k, p, q, r) and standard deviations when a Beta(1,3) distribution is generated-----29\nTable 4.10 The values of P(goodness-of-fit test accept │k, p, q, r) and standard deviations when a Beta(1,4) distribution is generated-----29\nTable 4.11 The values of P(goodness-of-fit test accept │k, p, q, r) and standard deviations when a Beta(2,3) distribution is generated-----30\nTable 4.12 The values of P(goodness-of-fit test accept │k, p, q, r) and standard deviations when a Beta(1,5) distribution is generated-----30\nTable 4.13 The values of P(goodness-of-fit test accept │k, p, q, r) and standard deviations when a Beta(2,4) distribution is generated-----31\nTable 4.14 The values of P(goodness-of-fit test accept │k, p, q, r) and standard deviations when a Beta(1,6) distribution is generated-----31\nTable 4.15 The values of P(goodness-of-fit test accept │k, p, q, r) and standard deviations when a Beta(3,4) distribution is generated-----32\nTable 4.16 The values of P(goodness-of-fit test accept │k, p, q, r) and standard deviations when a Beta(2,5) distribution is generated-----33\nTable 4.17 The values of P(goodness-of-fit test accept │k, p, q, r) and standard deviations when a Beta(1,7) distribution is generated-----33\nTable 4.18 The values of P(goodness-of-fit test accept │k, p, q, r) and standard deviations when a Beta(3,5) distribution is generated-----34\nTable 4.19 The values of P(goodness-of-fit test accept │k, p, q, r) and standard deviations when a Beta(2,6) distribution is generated-----35\nTable 4.20 The values of P(goodness-of-fit test accept │k, p, q, r) and standard deviations when a Beta(2,7) distribution is generated-----36\nTable 4.21 The values of P(goodness-of-fit test accept │k, p, q, r) and standard deviations when a Beta(4,1) distribution is generated-----38\nTable 4.22 The values of P(goodness-of-fit test accept │k, p, q, r) and standard deviations when a Beta(4,2) distribution is generated-----38\nTable 4.23 The values of P(goodness-of-fit test accept │k, p, q, r) and standard deviations when a Beta(5,1) distribution is generated-----39\nTable 4.24 The values of P(goodness-of-fit test accept │k, p, q, r) and standard deviations when a Beta(5,2) distribution is generated-----39\nTable 4.25 The values of P(goodness-of-fit test accept │k, p, q, r) and standard deviations when a Beta(4,3) distribution is generated-----40\nTable 4.26 The values of P(goodness-of-fit test accept │k, p, q, r) and standard deviations when a Beta(6,1) distribution is generated-----41\nTable 4.27 The values of P(goodness-of-fit test accept │k, p, q, r) and standard deviations when a Beta(7,1) distribution is generated-----41\nTable 4.28 The values of P(goodness-of-fit test accept │k, p, q, r) and standard deviations when a Beta(5,3) distribution is generated-----42\nTable 4.29 The values of P(goodness-of-fit test accept │k, p, q, r) and standard deviations when a Beta(6,1) distribution is generated-----43\nTable 4.30 The mean frequencies And variances for the convergence using the criterion that the final interval length <0.001-----46 | zh_TW |
