《The Art of Simulation》

1Introduction1

2Sampling from a Distribution6

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

3More Sampling Methods31

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

4Random Number Tables43

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

5Random Number Generators50

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

6Pseudo-Random Numbers72

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

7Elementary Sampling Experiments85

7．1 Bivariate Distributions．90

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

8Flow Diagrams94

9Estimation100

10Simple Queueing Problems119

11Further Queue Problems136

12General Simulation Problems146

13Design of Simulation Experiments171

References180

Index183