Potential Occurrence Probability
Reference - Discharging Reoccurrence Distribution, Average Rate of Reoccurrence Distribution, Generalized Average Rate of Reoccurrence, Potential Reoccurrence Probability
Potential Occurrence Probability - y = 1 - e -(x / m)
x - draw difference or Dd between previous occurrence and next draw number
m - average rate of reoccurrence
y - probability of occurrence relative to last occurrence
The potential occurrence probability was derived from the discharging reoccurrence function and the potential reoccurrence probability function. This function can be used to calculate the probability that a number will occur relative to the last occurrence. Occurrence and reoccurrence are compliments of each other; they are similar but not the same. Example, referencing the number 17 in the Wisconsin Megabucks 6/49 lottery, the last occurrence was at draw index 1491 based on a total draw count of 1500. What's the probability of 17 occurring in the next draw, 1501, or the up coming draw 1504 this 2006-11-11?
For 1501:
x = Dd = (1501 - 1491) = 9
m = Ag(49, 6) = 49 / 6 » 8.17
y = 1 - e -(9 / 8.17) » .668 or about 66.8%
For 1504:
x = Dd = (1504 - 1491) = 13
m = Ag(49,6) = 49 / 6 » 8.17
y = 1 - e -(13 / 8.17) » .796 or about 79.6%
The probability is low just after a number is picked and increases as the draw difference increases. However, this does not mean the probability of the number is more likely to be picked, it's a relative probability from the previous occurrence. There is another function that describes the probability of reoccurrence that is a compliment of this function. That function is defined in a different topic, Potential Reoccurrence Probability.
