# Thread: Finding criteria for a household financial budget falsification

1. ## 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.

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

Thank you so much for your helps.

2. ## Re: Finding criteria for a household financial budget falsification

I don't quite understand what you're trying to do, but I think you need to input a number into your system. Here's why: Consider two households, Alice and Bob. Alice reports a surplus of P=2 based on income of $11,023 and expenses of$11,021. Your research finds that her expenses are only $11,019, so her actual surplus is R=4. I think we can agree that Alice is truthful. Bob reports a surplus of P=20,000 based on income of$30,000 and expenses of $10,000. Your research finds that his income is actually$50,000, so his actual surplus is R=40,000. I think we can agree that Bob is falsifying his income.

Both of your examples of criterion depend only on the ratio of P and R, so that Bob and Alice have the same output.

- Hollywood

3. ## Re: Finding criteria for a household financial budget falsification

Originally Posted by hollywood
I don't quite understand what you're trying to do, but I think you need to input a number into your system. Here's why: Consider two households, Alice and Bob. Alice reports a surplus of P=2 based on income of $11,023 and expenses of$11,021. Your research finds that her expenses are only $11,019, so her actual surplus is R=4. I think we can agree that Alice is truthful. Bob reports a surplus of P=20,000 based on income of$30,000 and expenses of $10,000. Your research finds that his income is actually$50,000, so his actual surplus is R=40,000. I think we can agree that Bob is falsifying his income.

Both of your examples of criterion depend only on the ratio of P and R, so that Bob and Alice have the same output.

- Hollywood

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)?

Thanks.

4. ## Re: Finding criteria for a household financial budget falsification

Originally Posted by hollywood
I don't quite understand what you're trying to do, but I think you need to input a number into your system. Here's why: Consider two households, Alice and Bob. Alice reports a surplus of P=2 based on income of 11,023 and expenses of 11,021. Your research finds that her expenses are only 11,019, so her actual surplus is R=4. I think we can agree that Alice is truthful.

Bob reports a surplus of P=20,000 based on income of 30,000 and expenses of 10,000. Your research finds that his income is actually 50,000, so his actual surplus is R=40,000. I think we can agree that Bob is falsifying his income.

Both of your examples of criterion depend only on the ratio of P and R, so that Bob and Alice have the same output.

- Hollywood
Sorry about the formatting in my previous post. It looks like it was interpreting the dollar signs LaTeX start and stop - I thought we had to use bracket-TEX. Anyway....

Your two formulas calculate different things.

If P>0 and R>0 : Criterion = R-P/R
If P<0 and R<0 : Criterion = (abs(P)-abs(R)) / abs(P) = (-P-(-R))/(-P) = P-R/P

In the first case, you're using R as the starting place and finding out how much lower P is. In the second case, you're using P as the starting place and finding out how much higher (less negative) R is.

For your example P=-20 and R=40, using R as the starting place would suggest an output of 1.5 and using P as the starting place would suggest an output of 3.0.

- Hollywood

5. ## Re: Finding criteria for a household financial budget falsification

Originally Posted by hollywood
Sorry about the formatting in my previous post. It looks like it was interpreting the dollar signs LaTeX start and stop - I thought we had to use bracket-TEX. Anyway....

Your two formulas calculate different things.

If P>0 and R>0 : Criterion = R-P/R
If P<0 and R<0 : Criterion = (abs(P)-abs(R)) / abs(P) = (-P-(-R))/(-P) = P-R/P

In the first case, you're using R as the starting place and finding out how much lower P is. In the second case, you're using P as the starting place and finding out how much higher (less negative) R is.

For your example P=-20 and R=40, using R as the starting place would suggest an output of 1.5 and using P as the starting place would suggest an output of 3.0.

- Hollywood
Yes. Your are right. this is exactly my problem. I'm searching for a general criterion that can handle all situations without any different as you said.

Thanks.