Hi everyone, some of you may have seen my last post where I made a model for HOGE that showed the amount of coins being burned as the total transaction volume (V) increased.

I've done some more work on it to make it more realistic. Instead of making the model in terms of total transaction volume (V), I've made it in terms of quantity of transactions (Q). I've also moved the model from Excel over to MATLAB so I can more easily tweak it.

Definitions

 Q  - Total number of transactions
 V  - Total transaction volume
 dV - Single transaction volume
 Sb - Supply of HOGE burned
 Sc - Supply of HOGE in circulation
 Tb - Burn tax
 Tr - Redistribution tax

Properties

limit of V  as Q approaches infinity is ~34.5 trillion.
limit of dV as Q approaches infinity is 0.
limit of Tb as Q approaches infinity is 2%.
limit of Tr as Q approaches infinity is 0%.
limit of Sb as Q approaches infinity is 1 trillion.
limit of Sc as Q approaches infinity is 0.

How the Data was Generated

I generated data for 30 million transactions. For each transaction, I determined the single transaction volume (dV) by taking a random percentage (between 0% and 0.03%) of the current supply in circulation (Sc).

Limitations of the Model

- As you can see in the plot of dV, each transaction was a random volume between 0% and 0.03% of Sc. However, most transactions that happen within the market are not actually that random. In fact, they most likely closely follow a probability distribution.

- This model doesn't account for the number of HOGE holders increasing as well as various other market factors (i.e., price, being listed on exchanges, and being accepted by retailers). I assume that as the number of holders increases, the transaction volumes will go down, but also the frequency of transactions will go up. Retail adoption would also accelerate this.

I'd like to account for all the things above in my next revision, but I haven't quite figured out how to export all the HOGE data using ethereum-etl yet, haha. If you'd like to help me out with that, please message me.

Observations

It appears the graphs could be modeled/fitted very closely with logarithmic/exponential decay functions. I didn't get around to doing that yet, but that could be cool.

HOGE Plots:

- V and dV vs. Q

- Sc and Sb vs. Q

- Tr and Tb vs. Q

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If you'd like me to send you my MATLAB code and what not, message me your email and I'll send it all over to you.