# Finding criteria for a household financial budget falsification

I’m working on a financial problem about budget of households. Households in a state fill a form about their net budget in every year and our insurance company investigate their financial status and find the exact amount of their budget. The net budget can be positive or negative. I’m designing a system with neural network that we can find the households that Falsify their net budget, So my output is a binary [ 0 and 1] which 1 is false net budget and 0 is true net budget.

Suppose that households’ net budget is P and our investigated outcome of net budget is R. As you know :

R>=P


Now we have this:

If P=R then  :  Criterion = 0 (true net budget)
If P>0 and R>0   :  Criterion = R-P/R
If P<0 and R<0   :  Criterion = (abs(P)-abs(R)) / abs(P)
If P<0 and R>0    :  ????     (A lot of households have this situation and I dint find any criterion for it)
If P<0 and R=0    :  ????     (Some of households have this situation and I dint find any criteria for it)
If P=0 and R>0    :  ????      (Some of households have this situation and I dint find any criterion for it)


After finding these criterion that must be between 0 and 1 [0 1], I set a threshold (like 0.5), If the criterion is higher than 0.5 household is falsifying the net budget (output = 1) and If it is lower than 0.5 we have a true budget and there isn’t any problem in budget declaring of households (output = 0).

** In range of [0 1], if falsification is higher (depends of above functions - P and R) the creation goes toward 1 and if the household is honest it goes toward 0. So every household (sample) has a criterion between 0 and 1.

My main problem is finding a good criterion when (P<0 , R>0), After that (P<0 , R=0) and finally (P=0 , R>0). IF I have a problem in first, second and third criterion, feel free to say. I think the output of second situation is different from third because structures of criteria is different. I’m going to find a single criterion function If it is possible.

Example : First conduction : P = 10 , R = 15 : Criteria : (15-10/15) = 33.3% ( falsification rate for this household ) Second conduction : P = -16, R = -10 : Criteria : (abs(-16)-abs(-10))/abs(-16) = 37.5% ( falsification rate for this household )

Now if for example P=-20 and R = 40, How we can calculate falsification rate? . This is main question. after that how we can calculate when (P<0 , R=0) and finally (P=0 , R>0)?

I check this criterion with this procedure: for example in first criterion when P>0 and R>0 we have P = 5 and R = 10 so E = 50% . Now if P=fix = 5 and R=increase ( for example now R= 20) we have E = 75%. This is true conceptually in our problem. We must have more falsification when P=5 and R=20 Compared with P = 5 and R = 10 . + we must check it when R=fix and P=increase (or decrease).

PS. I Have 2000 samples with different size of P and R.

Thank you so much for your helps.

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