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Random Number Transforms - Reoccurrence Distribution

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JADELottery's avatar - MeAtWork 03.PNG
The Quantum Master
West Concord, MN
United States
Member #21
December 7, 2001
3675 Posts
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Posted: December 7, 2006, 11:24 am - IP Logged

Random Number Transforms - Reoccurrence Distribution

    Reference - Discharging Reoccurrence Distribution

    Random Reoccurrence Distribution -    x = -m ln(1 - y)

    m - average rate of reoccurrence
    y - random number, 0 £ y < 1

    x as analog - values of x are not rounded to any decimal place value.
    x as digital - values of x are converted to the integer part of x.
                Ex.1 -    4.129840012394543 is converted to 4
                Ex.2 -    2.781992014293572 is converted to 2
                valid digital values of x are when x ³ 1

VB Code for Random Reoccurrence Distribution

Function Rand_RD(m) As Long 'average rate of reoccurrence - m

    If m >= 1 Then 'rate of reoccurrence must be 1 or more

      Do

          x = Int(-1 * m * Log(1 - Rnd)) 'get random integer x value

      Loop Until x > 0 'if x is 0 or less, resample for x

      Rand_RD = x

    Else 'set Rand_RD to 1 if rate of reoccurrence is less than 1

      Rand_RD = 1

    End If

End Function

 

1500 Random Samples, m = 8.17
8, 3, 5, 3, 5, 2, 6, 17, 13, 4, 5, 27, 29, 3, 5, 19, 8, 24, 11, 5, 9, 5, 5, 11, 8, 1, 10, 8, 3, 2, 7, 1, 5, 6, 15, 26, 1, 1, 13, 4, 9, 4, 9, 9, 10, 3, 5, 9, 1, 5, 12, 2, 8, 4, 13, 6, 14, 6, 8, 3, 10, 24, 1, 1, 16, 10, 4, 5, 7, 6, 3, 3, 9, 12, 3, 3, 10, 10, 9, 6, 4, 9, 3, 16, 5, 11, 4, 2, 8, 7, 1, 2, 6, 6, 21, 2, 1, 7, 4, 32, 13, 10, 4, 29, 17, 12, 13, 1, 3, 12, 35, 4, 2, 7, 8, 6, 5, 20, 14, 2, 3, 3, 14, 24, 2, 2, 2, 18, 5, 11, 2, 6, 8, 11, 1, 11, 3, 2, 6, 1, 10, 8, 12, 9, 1, 1, 1, 7, 4, 8, 7, 8, 8, 13, 5, 2, 1, 10, 3, 5, 4, 3, 11, 1, 3, 15, 2, 16, 1, 17, 2, 4, 12, 2, 1, 31, 10, 8, 4, 4, 7, 44, 14, 10, 31, 2, 13, 3, 3, 30, 5, 7, 9, 3, 24, 17, 30, 2, 19, 8, 1, 1, 1, 13, 1, 2, 6, 15, 5, 2, 6, 10, 23, 14, 6, 29, 8, 1, 2, 4, 9, 17, 5, 1, 9, 6, 3, 2, 2, 18, 4, 19, 7, 11, 1, 6, 11, 9, 22, 20, 1, 11, 1, 5, 3, 23, 17, 3, 3, 9, 27, 6, 5, 10, 9, 5, 1, 1, 9, 2, 9, 6, 22, 10, 4, 3, 20, 22, 15, 34, 6, 3, 2, 30, 20, 9, 33, 1, 3, 10, 23, 21, 20, 1, 25, 10, 3, 4, 10, 9, 10, 3, 25, 25, 5, 1, 3, 11, 13, 15, 4, 37, 8, 2, 3, 2, 16, 2, 8, 1, 6, 20, 17, 9, 2, 4, 8, 6, 2, 5, 11, 33, 1, 2, 2, 10, 12, 9, 2, 8, 12, 3, 16, 15, 9, 5, 35, 8, 6, 26, 5, 3, 3, 6, 4, 5, 15, 5, 10, 9, 4, 3, 9, 4, 2, 38, 1, 3, 8, 9, 3, 2, 5, 5, 7, 4, 8, 8, 28, 15, 28, 15, 5, 26, 1, 28, 12, 6, 8, 5, 2, 12, 4, 2, 4, 2, 5, 4, 6, 4, 1, 13, 32, 6, 1, 1, 2, 3, 19, 14, 4, 20, 1, 1, 26, 6, 3, 5, 40, 11, 16, 19, 4, 2, 9, 5, 3, 10, 2, 5, 7, 3, 3, 1, 5, 1, 16, 1, 12, 13, 18, 12, 9, 16, 1, 1, 6, 1, 15, 2, 3, 12, 7, 3, 10, 1, 22, 24, 5, 1, 8, 4, 3, 1, 4, 2, 5, 17, 10, 1, 14, 26, 25, 4, 7, 1, 2, 15, 5, 24, 57, 3, 10, 4, 10, 1, 12, 8, 6, 9, 12, 18, 21, 13, 4, 18, 23, 6, 1, 2, 1, 9, 15, 1, 15, 11, 10, 12, 1, 15, 6, 1, 5, 3, 13, 6, 1, 2, 11, 8, 2, 1, 9, 13, 9, 7, 1, 14, 5, 13, 10, 3, 4, 4, 1, 15, 7, 42, 6, 24, 1, 3, 1, 17, 1, 12, 2, 6, 6, 2, 4, 18, 7, 1, 13, 9, 1, 2, 2, 24, 17, 2, 20, 1, 6, 6, 25, 7, 16, 5, 22, 1, 1, 12, 9, 1, 1, 27, 11, 4, 1, 4, 1, 3, 8, 17, 15, 1, 7, 21, 1, 5, 15, 14, 4, 18, 15, 16, 1, 14, 9, 5, 13, 2, 10, 8, 10, 32, 5, 3, 44, 3, 1, 2, 10, 11, 9, 19, 3, 6, 12, 1, 1, 15, 5, 4, 3, 12, 1, 13, 11, 1, 10, 14, 6, 10, 6, 1, 1, 5, 5, 30, 8, 26, 6, 4, 6, 7, 25, 1, 1, 2, 4, 11, 5, 54, 11, 6, 3, 10, 9, 18, 1, 6, 9, 18, 2, 2, 5, 5, 7, 9, 3, 20, 15, 2, 8, 2, 7, 6, 6, 3, 5, 9, 1, 26, 3, 2, 19, 4, 2, 1, 6, 10, 7, 2, 3, 6, 18, 10, 3, 3, 12, 19, 18, 7, 11, 35, 21, 30, 4, 17, 17, 34, 3, 2, 2, 10, 16, 7, 1, 8, 12, 6, 14, 3, 4, 3, 11, 8, 3, 6, 3, 15, 6, 20, 4, 8, 26, 5, 5, 10, 1, 1, 27, 15, 5, 2, 1, 17, 6, 1, 15, 15, 6, 7, 22, 2, 1, 11, 17, 4, 47, 1, 3, 5, 6, 13, 14, 5, 4, 7, 8, 18, 2, 17, 19, 12, 25, 6, 7, 3, 2, 3, 4, 17, 17, 5, 9, 18, 5, 1, 2, 2, 19, 5, 8, 9, 10, 11, 7, 5, 2, 17, 3, 7, 22, 8, 9, 4, 2, 2, 2, 3, 15, 6, 3, 6, 16, 7, 11, 3, 9, 2, 26, 20, 10, 7, 1, 18, 4, 1, 9, 6, 6, 19, 11, 13, 18, 1, 12, 11, 13, 12, 2, 4, 8, 4, 5, 4, 4, 25, 1, 12, 4, 1, 1, 3, 5, 4, 3, 7, 9, 18, 2, 10, 2, 4, 4, 1, 17, 16, 17, 5, 1, 27, 2, 23, 6, 9, 9, 1, 8, 5, 6, 5, 21, 1, 14, 25, 34, 5, 3, 4, 15, 8, 9, 3, 4, 5, 3, 5, 7, 2, 9, 13, 11, 16, 7, 3, 14, 5, 9, 1, 9, 10, 16, 3, 1, 3, 21, 17, 6, 11, 4, 2, 20, 5, 15, 29, 9, 8, 1, 3, 3, 1, 6, 1, 11, 5, 9, 5, 4, 38, 5, 34, 5, 2, 13, 14, 3, 14, 33, 2, 4, 3, 2, 2, 7, 6, 4, 17, 4, 3, 4, 4, 3, 7, 5, 14, 16, 32, 4, 12, 6, 15, 16, 7, 7, 20, 2, 9, 6, 18, 4, 1, 5, 1, 25, 7, 16, 3, 24, 3, 2, 6, 11, 3, 7, 2, 10, 6, 8, 8, 5, 3, 19, 14, 10, 1, 14, 2, 5, 8, 2, 24, 1, 3, 10, 4, 7, 13, 4, 3, 3, 5, 10, 6, 3, 3, 13, 15, 10, 8, 1, 3, 19, 3, 1, 5, 6, 1, 12, 2, 3, 36, 1, 52, 29, 10, 1, 20, 11, 5, 1, 8, 13, 21, 1, 12, 20, 2, 3, 9, 2, 8, 5, 12, 4, 5, 14, 3, 4, 8, 29, 1, 4, 1, 12, 9, 3, 27, 3, 60, 8, 4, 6, 6, 11, 6, 7, 5, 4, 15, 3, 7, 5, 3, 5, 1, 14, 3, 40, 3, 1, 2, 5, 4, 5, 14, 16, 50, 1, 6, 14, 4, 12, 2, 1, 1, 4, 6, 3, 13, 19, 1, 3, 2, 2, 3, 14, 2, 1, 2, 4, 11, 11, 8, 1, 8, 12, 11, 11, 2, 5, 2, 16, 2, 1, 18, 17, 4, 4, 3, 6, 2, 9, 5, 12, 2, 15, 13, 6, 8, 13, 2, 6, 7, 1, 7, 26, 7, 18, 6, 53, 9, 3, 10, 12, 3, 2, 9, 3, 1, 8, 20, 6, 1, 6, 5, 12, 2, 2, 2, 4, 5, 1, 8, 9, 10, 1, 3, 2, 1, 10, 3, 28, 1, 3, 8, 6, 13, 3, 2, 5, 5, 5, 3, 12, 5, 1, 8, 7, 3, 8, 4, 28, 29, 7, 6, 8, 2, 13, 7, 9, 19, 6, 3, 4, 3, 7, 18, 1, 6, 2, 2, 8, 3, 4, 8, 2, 6, 7, 2, 7, 6, 2, 3, 5, 10, 2, 18, 9, 4, 10, 6, 5, 30, 8, 6, 4, 4, 7, 12, 14, 4, 7, 1, 11, 6, 1, 2, 1, 1, 1, 11, 19, 3, 14, 10, 11, 6, 9, 16, 19, 6, 12, 10, 5, 11, 4, 4, 10, 3, 9, 18, 17, 34, 3, 7, 8, 12, 1, 17, 21, 26, 3, 2, 5, 6, 20, 3, 1, 1, 3, 1, 19, 1, 22, 5, 2, 7, 5, 1, 7, 10, 3, 2, 1, 1, 16, 4, 2, 5, 2, 7, 11, 2, 3, 8, 18, 6, 2, 7, 9, 3, 8, 3, 12, 2, 8, 6, 23, 3, 12, 12, 8, 7, 5, 19, 19, 2, 2, 17, 3, 5, 6, 10, 6, 8, 25, 3, 3, 2, 6, 25, 7, 4, 13, 13, 2, 18, 1, 4, 5, 22, 1, 2, 2, 6, 1, 1, 23, 14, 13, 7, 4, 42, 8, 12, 2, 3, 6, 11, 23, 7, 8, 27, 11, 9, 2, 15, 4, 5, 1, 9, 3, 3, 4, 1, 10, 42, 3, 14, 7, 11, 29, 12, 1, 1, 14, 23, 2, 18, 3, 5, 6, 2, 6, 16, 3, 6, 3, 3, 2, 4, 8, 4, 7, 2, 3, 19, 8, 9, 1, 2, 5, 6, 31, 12, 16, 8, 8, 3, 7, 5, 14, 10, 12, 7, 1, 9, 8, 12, 6, 5, 10, 10, 3, 10, 8, 17, 9, 41, 6, 8, 11, 7, 4, 7, 6, 24, 43, 1, 1, 8, 11, 6, 3, 3

 

Distribution of 1500 Random Samples, m = 8.17

Draw Difference Dd

Actual

Calculated

1

169

162.4471

2

141

143.7324

3

152

127.1738

4

105

112.5227

5

113

99.5596

6

108

88.0899

7

70

77.9415

8

78

68.9623

9

70

61.0175

10

62

53.988

11

47

47.7683

12

48

42.2652

13

34

37.396

14

31

33.0878

15

32

29.2759

16

24

25.9032

17

28

22.919

18

25

20.2787

19

21

17.9425

20

17

15.8754

21

9

14.0465

22

9

12.4283

23

9

10.9965

24

11

9.7296

25

12

8.6087

26

11

7.617

27

7

6.7394

28

5

5.963

29

8

5.2761

30

6

4.6682

31

3

4.1304

32

4

3.6546

33

3

3.2336

34

5

2.861

35

3

2.5314

36

1

2.2398

37

1

1.9818

38

2

1.7535

39

0

1.5514

40

2

1.3727

41

1

1.2146

42

3

1.0746

43

1

0.9508

44

2

0.8413

45

0

0.7444

46

0

0.6586

47

1

0.5827

48

0

0.5156

49

0

0.4562

50

1

0.4037

51

0

0.3572

52

1

0.316

53

1

0.2796

54

1

0.2474

55

0

0.2189

56

0

0.1937

57

1

0.1714

58

0

0.1516

59

0

0.1342

60

1

0.1187

 

Graph of Distribution for 1500 Random Samples, m = 8.17

Presented 'AS IS' and for Entertainment Purposes Only.
Any gain or loss is your responsibility.
Use at your own risk.

Order is a Subset of Chaos
Knowledge is Beyond Belief
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