|p Statistics: Variety of Digits|
When testing longer chains we gonna start with a simple question:|
How many DIFFERENT DIGITS are contained in a chain of length L?
Let us call this number the Variety of digits VOD.
Here is an example for p with L=5.
14159 -> VOD = 4
26535 -> VOD = 4
89793 -> VOD = 4
23846 -> VOD = 5
26433 -> VOD = 4
83279 -> VOD = 5
50288 -> VOD = 4
41971 -> VOD = 4
69399 -> VOD = 3
37510 -> VOD = 5
The construction law for the VOD-distribution is easy to find.
Let w(L,d) be the probability that a chain of length L consists of exactly d different digits.
For L=1 we have even one digit:
w(1,d)=1 for d=1
w(1,d)=0 for d>1
For L>1 any w(L,d) can be calculated from its predecessor:
w(L+1,d) = w(L,d) x d/10 + w(L,d-1) x (10-d)/10
Finding a VOD=1 for L=5 is just the same as searching for a single digit run of length 5 (e.g. 11111).
But analyzing single digit runs is limited to L~7 due to the available data.
Thus testing variety of digits up to L=40 is a chance to get a better feeling for the regularity of single digit distribution. More than this the VOD can be an indicator for clusters.
|Digits analyzed: 4.2 * 10 9|
Analysis started at digit: 1
Ellapsed computer time for each L: 5 min
|Length of |
for the VOD
|Number of statistical |