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