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The 490, and other starting character patterns

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• The 490, and other starting character patterns

• RE: The 490, and other starting character patterns

  Jorge_Stolfi > 29-09-2025, 11:11 PM

  (29-09-2025, 10:50 PM)SherriMM Wrote: You are not allowed to view links. Register or Login to view.Also my statistics only include the 18 line-initial characters, not any amount of random letters. Of the 18 characters, should I compute based on frequency?

  
  If you assume that those 18 characters are equally likely then P(q) = P(o) = P(y) = 1/18 = ~0.056.  Then, if each line-initial letter is just chosen at random, independently, in 1000 lines you would expect 998*(1/18)^3 = 0.18 occurrences of qoy; that is none, or maybe one or two.
  
  But suppose that (say) P(q) = P(o) = P(y) = 0.30, with all the other 15 letters occurring only on 10% of the lines.  Then in 1000 lines, with each initial being chosen at random and independently, you should expect 998*(0.30)^3 = ~27 occurrences of qoy.  
  
  Thus, in order to tell whether the number of qoy occurences is anomalous, you must consider the actual frequencies of the letters in line-initial positions.
  
  And, again, note that some three-glyph sequences will be more common that what the formula says.  For instance, in the second example above, the string qoy may occur only  25 times, but qyo may occur 31 times, oqy 26 times, oyq 33 times...  If you pick the the most common three-letter pattern, that pattern will be more common than expected.
  
  All the best, --jorge

• RE: The 490, and other starting character patterns

  RobGea > 30-09-2025, 12:25 AM

  Some numbers from RF1b-er.txt
  

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  Code:

  First_letter_of_a_line counts from RF1b-er.txt
Total first_letter_of_a_line character Tokens: 4130
How many distinct characters: 16

Eva Count Percentage  Relative_frequency

d  640    15.4964%      rf: 0.155
s  624    15.109%      rf: 0.1511
y  610    14.77%        rf: 0.1477
o  544    13.1719%      rf: 0.1317
q  531    12.8571%      rf: 0.1286
t  399    9.661%      rf: 0.0966
p  374    9.0557%      rf: 0.0906
c  160    3.8741%      rf: 0.0387
k  100    2.4213%      rf: 0.0242
l  69    1.6707%      rf: 0.0167
f  41    0.9927%      rf: 0.0099
a  20    0.4843%      rf: 0.0048
r  13    0.3148%      rf: 0.0031
e  3      0.0726%      rf: 0.0007
x  1      0.0242%      rf: 0.0002
?  1      0.0242%      rf: 0.0002
---

• RE: The 490, and other starting character patterns

  Jorge_Stolfi > Today, 05:43 AM

  (30-09-2025, 12:25 AM)RobGea Wrote: You are not allowed to view links. Register or Login to view.

  Code:

  First_letter_of_a_line counts from RF1b-er.txt
Total first_letter_of_a_line character Tokens: 4130

d  640    15.4964%      rf: 0.155
s  624    15.109%      rf: 0.1511
y  610    14.77%        rf: 0.1477
o  544    13.1719%      rf: 0.1317
q  531    12.8571%      rf: 0.1286
...

  
  OK, so (n-2)P(q)P(o)P(y) = 4128 * 0.129 * 0.132 * 0.148 = ~10.4.
  
  Meaning that, if the line-initial letters had been chosen randomly and independently with those frequencies, in those 4130 lines you should expect to get 10 qoy or thereabouts.  
  
  Also about a dozen dsy, a dozen sdy, a dozen yds, ten qyd, ...
  
  All the best, --jorge

• RE: The 490, and other starting character patterns

  RadioFM > 29 minutes ago

  If intentionally interspersing by not repeating previous character, expected number of qoy occurrences ~13.6
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