|Posted: November 10, 2006, 5:41 am - IP Logged|
First and Second Order Work Equations
Reference - Potential Reoccurrence Probability, Potential Occurrence Probability, Half-life of Reoccurrence
First Order Work Equation - y = 4 (e -(x / m) - e -(2 x / m) )
Second Order Work Equation - y = 16 (e -(x / m) - 5 e -(2x / m) + 8 e -(3x / m) - 4 e -(4x / m) )
x - draw difference or Dd between last occurrence and some future draw number
m - average rate of reoccurrence
second order region 1 - 0 £ x £ -m ln(1 / 2)
second order region 2 - -m ln(1 / 2) £ x £ ¥
The first and second order work equations are related to the potential reoccurrence and occurrence probabilities. Most of the work done by random selection is centered around the first half-life of reoccurrence. The closer the draw difference is to the first half-life of reoccurrence, there is a better equal probability of reoccurrence and occurrence selection. The first order work equation is like a probability function, it shows the relative closeness to the first half-life of reoccurrence. The second order work equation operates in contrast to the first order work equation. The second order work equation has two regions of draw difference that is operates. The first region is 0 to the first half-life of reoccurrence and the second is the first half-life of reoccurrence to ¥. The first region captures draw differences that are just after the number's selection. The second region captures draw differences that are heading to a long out from the number's selection.
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