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I'm trying to craft an example going through the math equation in Section 4.1 . I'm trying to show my work. Can you tell me if I've got it right and if not, help correct me?
Hx – Cumulative weight at node x – Let’s say 65
Hy – Cumulative weight at node y – Let’s say 70
Hz – Cumulative weight at node z – Let’s say 75
α – Try with 1
Pxy = exp( -1( 65 – 70 ) * ((75+74+…65)^(-1(65 – 75)) )^-1
Pxy = exp( 5) * (770^10))^-1
Pxy = 1.365e-29^5
Pxy = 4.737e-145
Unfortunately, this doesn't look correct. Regardless of the actual numbers, you are not treating the sum as a sum but rather as a single summand. On top of that, you seem to be missing the exp function in a few places during your P_xy calculation.
Below I am pasting a sample calculation for a transaction x that is referenced by three other transactions y_1,y_2,y_3. That is, y_i⇝x for i=1,2,3.
So for example, the transition probability of going from x to y_3 is ≈ 32%.
x should be larger than the one of y. Secondly, neither ((75+74+…65)^(-1(65 – 75)))^-1 nor 75^( -1(65 - 75) + 74^(-1(65 - 75) has the exp function in it, so I am really not sure what you are calculating.