The Art of SimulationPDF电子书下载

1 Introduction 1

2 Sampling from a Distribution 6

2．1 Introduction． 6

2．2 The ＇Top Hat＇ Method． 7

2．3 A Mechanised Version of the ＇Top Hat＇ Method． 10

2．4 The Method of Mixtures． 22

2．5 The Rejection Procedure． 24

2．6 Bivariate Sampling． 27

2．7 Multivariate Sampling． 28

2．8 Sampling under Dependence． 29

3 More Sampling Methods 31

3．1 Normal Distribution． 31

3．2 The x2 or Gamma Distribution． 34

3．3 Exponential Distribution． 35

3．4 The Poisson Distribution． 36

3．5 Other Rejection Techniques． 37

3．6 The Binomial Distribution． 39

3．7 Selecting a Point at Random in an n-dimensional Volume． 41

4 Random Number Tables 43

4．1 Introduction and History． 43

4．2 Tests of Random Number Tables． 44

4．3 Frequency Test． 44

4．4 The Serial Test． 45

4．5 The Poker Test． 45

4．6 The Gap Test． 46

4．7 The Run Test． 46

4．8 Yule＇s Test． 47

4．9 The D2 Test． 47

4．10 Comments Concerning Tests． 47

4．11 Tables of Other Random Variates． 48

4．12 Conclusion． 48

5 Random Number Generators 50

5．1 Introduction． 50

5．2 The Electronic Machines． 52

5．3 ERNIE． 53

5．4 The Rand Corporation Machine． 55

5．5 The Manchester Mark I Computer Randomising Unit． 56

5．6 The United Steel Companies Random Number Generator． 56

5．7 The General Electric Electronic Probability Generator． 61

5．8 The Lion Random Selector． 64

5．9 The R．C．A．Random Number Generator． 65

5．10 Analogue Randomisers． 66

5．11 Pseudo-random Number Generators． 67

6 Pseudo-Random Numbers 72

6．1 The Mid-square Technique． 73

6．2 The Mid-product Method． 74

6．3 The Lehmer Congruence Method． 75

6．4 Second-order Recurrence Processes． 81

6．5 Tests on Pseudo-random Numbers． 83

7 Elementary Sampling Experiments 85

7．1 Bivariate Distributions． 90

7．2 Improving the Accuracy of Estimation of Sampling Distributions． 90

8 Flow Diagrams 94

9 Estimation 100

10 Simple Queueing Problems 119

11 Further Queue Problems 136

12 General Simulation Problems 146

13 Design of Simulation Experiments 171

References 180

Index 183