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Math Help - Finding criteria for a household financial budget falsification

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    Lightbulb Finding criteria for a household financial budget falsification

    Iím 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. Iím 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 householdsí 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 isnít 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. Iím 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.

    * I send same question in calculates page. I think here is more appropiate for this question. If this is true please remove the calculus page question. thanks
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    Re: Finding criteria for a household financial budget falsification

    **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)?
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    MHF Contributor ebaines's Avatar
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    Re: Finding criteria for a household financial budget falsification

    The problem is that the "size" of a budget is not the net plus-or-minus cash flow, but rather should be based on either the amount of income or the amount of expenses. Let me give you an example: suppose a household has a budget of income = \$10,000 and expenses = \$9,999, for P = +\$1, and suppose in reality it turns out that R= \$5; being accurate to \$5 on income and expenses of this magnitude is quite good, but your criterion would claim the budget to be false, as (R-P)/R = (5-1)/5 = 0.8. On the other hand if on that same income of \$10,000 they planned expenses of only \$5,000 then P = \$5000, and if R turned out to be \$6,000 (off by \$1,000) your criterion yields (6000-5000)/6000 = 0.167. So the budget with the much larger error passes as true. In effect you reward prople whose budget has either a large surplus or a large deficit, and penalize those who predict close to \$0 deficit or surplus. I would suggest that rather than looking at just P and R, consider P/I and R/I, where I is income before expenses, and if |(R-P)/I| is less than, say, 5% then they had a budget that you can say was true.
    Last edited by ebaines; June 6th 2014 at 09:40 AM.
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    Re: Finding criteria for a household financial budget falsification

    Quote Originally Posted by ebaines View Post
    The problem is that the "size" of a budget is not the net plus-or-minus cash flow, but rather should be based on either the amount of income or the amount of expenses. Let me give you an example: suppose a household has a budget of income = $10,000 and expenses = $9,999, for P = +$1, and suppose in reality it turns out that R= $5; being accurate to $5 on income and expenses of this magnitude is quite good, but your criterion would claim the budget to be false, as (R-P)/R = (5-1)/5 = 0.8. On the other hand if on that same income of $10,000 they planned expenses of only $5,000 then P = $5000, and if R turned out to be $6,000 (off by $1,000) your criterion yields (6000-5000)/6000 = 0.167. So the budget with the much larger error passes as true. In effect yuo reward prople whose budget has either a large surplus or a large deficit, and penalize those who predict close to $0 deficit or surplus. I would suggest that rather than looking at just P and R, consider P/I and R/I, where I is income before expenses, and if |(R-P)/I| is less than, say, 5% then they had a budget that you can say was true.
    Thank you so much for answer. that is true but every household has special parameters ( financial ratios ) that these parameters are my system's input and true or false situation is my system's output. So I have various households and various outputs. For a household that has a low values like P=1 and R=5 , finding R = 80% is correct in the scale of these two numbers. I think when we concentrate on size we can say that my criteria is true, Because my system take intro account size of households as inputs for training. Is this true?

    Otherwise my main question is when (P<0 , R>0), After that (P<0 , R=0) and finally (P=0 , R>0). How can I handle these conditions?

    PS. Amount of falsification isn't in portent in this case because we consider size of households as an import variable of system and in our system we have various households with differences 'P' and 'R'. Main problem is a general criterion for every conditions of 'P' and 'R' values. What do you think?

    Thank you again.
    Last edited by jacks12; June 6th 2014 at 09:36 AM.
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    MHF Contributor ebaines's Avatar
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    Re: Finding criteria for a household financial budget falsification

    Quote Originally Posted by jacks12 View Post
    I think when we concentrate on size we can say that my criteria is true, Because my system take intro account size of households as inputs for training. Is this true?
    I have no idea whether it's true or not - perhaps if you gave some examples it would help me understand what you're getting at.

    Quote Originally Posted by jacks12 View Post
    Otherwise my main question is when (P<0 , R>0), After that (P<0 , R=0) and finally (P=0 , R>0). How can I handle these conditions?
    How about using |(R-P)/(R+P)|? Note the absolute value notation. Then for the case where R+P = 0 score it a 1 (i.e. false) if R = -P and score it 0(true) if R=P=0.
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    Re: Finding criteria for a household financial budget falsification

    Quote Originally Posted by ebaines View Post
    I have no idea whether it's true or not - perhaps if you gave some examples it would help me understand what you're getting at.



    How about using |(R-P)/(R+P)|? Note the absolute value notation. Then for the case where R+P = 0 score it a 1 (i.e. false) if R = -P and score it 0(true) if R=P=0.

    I want check your proposed criterion : ( Numerator & Denominator divided by P )


    If P>0 and R>0 : if P=fix and R=increase >> E(Criterion) = increase (This is correct)
    If P>0 and R>0 : if P=increase and R=fix >> E(Criterion) = decrease (This is correct)

    If P<0 and R<0 : if P=increase (higher negative value) and R=fix >> E(Criterion) = decrease (This is correct)
    If P<0 and R<0 : if P=fix and R=increase(higher positive value) >> E(Criterion) = increase (This is correct)

    If P<0 and R>0 : if P=fix and R=increase >> E(Criterion) = increase (This is correct)
    If P<0 and R>0 : if P=increase(higher negative value) and R=fix >> E(Criterion) = decrease (This is wrong) >> We should have higher "E" in this case. In this case sometimes absolute value of 'R' is bigger than 'P' and sometimes absolute value of 'R' is smaller than 'P' // as you know in all cases R>=P .

    ** Is this criterion between 0 and 1?
    ** My problem is that i don't have income and expense of households now, I should check for gaining this database. You can propose another criterion with that basic beside my criteria that we are talking about ( adding 'I' in criterion ) if you can. It is really helpful to think about these two criteria before gaining new database if exists.

    Thank you very much for your kind and outstanding helps.
    Last edited by jacks12; June 6th 2014 at 11:01 AM.
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    MHF Contributor ebaines's Avatar
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    Re: Finding criteria for a household financial budget falsification

    Sorry, but I have no idea what you are saying. What does "( Numerator & Denominator divided by P )" mean? That was not my proposal, so I don't understand what you're getting at. Also what does this mean:

    Quote Originally Posted by jacks12
    "If P<0 and R>0 : if P=increase(higher negative value) and R=fix >> E(Criterion) = decrease (This is wrong) >> We should have higher "E" in this case)"
    Please clarify that with complete sentences. Also in your original post you said the criterion must be positive - so I don't understand what you mean by "E=decrease." Again - please show us some examples and it may be clearer.
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    Re: Finding criteria for a household financial budget falsification

    Quote Originally Posted by ebaines View Post
    Sorry, but I have no idea what you are saying. What does "( Numerator & Denominator divided by P )" mean? That was not my proposal, so I don't understand what you're getting at. Also what does this mean:



    Please clarify that with complete sentences. Also in your original post you said the criterion must be positive - so I don't understand what you mean by "E=decrease." Again - please show us some examples and it may be clearer.
    Yes. It must be positive and in the range of [0 1] . for example when P>0 and R>0 we have P = 5 and R = 10 so E = 33.33% . Now if P=fix = 5 and R=increase ( for example now R= 20) we have E = 60%. 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 .

    Another example when P<0 and R<0 we have P = -20 and R = -13 so E = 21.21% . Now if P=fix = -20 and R=increase ( for example now R= -5) we have E = 60%. This is true conceptually in our problem. We must have more falsification when P=-20 and R=-5 Compared with P = -20 and R = -13 .

    These are my procedures to check created criterion.
    Last edited by jacks12; June 6th 2014 at 11:31 AM.
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    Re: Finding criteria for a household financial budget falsification

    Quote Originally Posted by ebaines View Post
    Sorry, but I have no idea what you are saying. What does "( Numerator & Denominator divided by P )" mean? That was not my proposal, so I don't understand what you're getting at. Also what does this mean:



    Please clarify that with complete sentences. Also in your original post you said the criterion must be positive - so I don't understand what you mean by "E=decrease." Again - please show us some examples and it may be clearer.

    Sorry. I forgot to answer your first question:

    |(R-P)/(R+P)| = |(1-(P/R))/(1+(P/R))|

    It was only for checking effect of that procedure I mentioned ( fixing one item and increasing other on ) on criterion.

    Thank you again.
    Last edited by jacks12; June 6th 2014 at 09:56 PM.
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    Re: Finding criteria for a household financial budget falsification

    Quote Originally Posted by jacks12 View Post
    Yes. It must be positive and in the range of [0 1] . for example when P>0 and R>0 we have P = 5 and R = 10 so E = 33.33% . Now if P=fix = 5 and R=increase ( for example now R= 20) we have E = 60%. 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 .

    Another example when P<0 and R<0 we have P = -20 and R = -13 so E = 21.21% . Now if P=fix = -20 and R=increase ( for example now R= -5) we have E = 60%. This is true conceptually in our problem. We must have more falsification when P=-20 and R=-5 Compared with P = -20 and R = -13 .

    These are my procedures to check created criterion.
    Maybe we can work more on your proposed criterion R-P/I but if we find a criterion only with R and P it is so better for my system structure. What do you think ? Do you think R-P/I satisfy all conditions that I mentioned above? (P<0 and R>0) or (P<0 and R<0) . what is range of this new criterion ?

    Thanks.
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    Re: Finding criteria for a household financial budget falsification

    Quote Originally Posted by jacks12 View Post
    Sorry. I forgot to answer your first question:

    |(R-P)/(R+P)| = |(1-(P/R))/(1+(P/R))|

    It was only for checking effect of that procedure I mentioned ( fixing one item and increasing other on ) on criterion.

    Thank you again.
    About your previous criterion : (R-P)/I . Is this satisfy all conditions? : Suppose that >> I(income) - E(expenditure) = P , So we have these conditions :

    first // P>0 >> (I>E) and R>0 ***
    Second// P=0 >> (I=E) and R>0
    Third// P<0 >> ( I<E) and R>0 ***
    Fourth// P<0 >> ( IE) and R=0
    Fifth// P<0 >> (I<E) and R<0 ***

    You know in all cases R>=P and *** conditions are more important. As I said using only "p" and "R" for creating criteria is more suitable for my problem but we can improve and have this criteria besides that criteria. what is range of this formula?

    Thank you so much again.
    Last edited by jacks12; June 8th 2014 at 01:17 PM.
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    MHF Contributor ebaines's Avatar
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    Re: Finding criteria for a household financial budget falsification

    I suggested the absolute value of |(R-P)/I|. Since income I is always greater than or equal to the net budget this must be between 0 and 1. The further apart R and P are the greater the result. So I believe it meets all your requirements.
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    Re: Finding criteria for a household financial budget falsification

    Quote Originally Posted by ebaines View Post
    I suggested the absolute value of |(R-P)/I|. Since income I is always greater than or equal to the net budget this must be between 0 and 1. The further apart R and P are the greater the result. So I believe it meets all your requirements.
    thank you for your answer Ebaines.

    I have a comment on this criterion. That's true. It is always equal or greater than 0 but suppose that R-P is so great and greater than I.

    For example :
    I=10,000 E=1000 P=9,000 R=20,000 so we have : |(R-P)/I|=1.1

    This is my case. a lot of households has this condition and now this criteria can't satisfy upper bound (1) .

    Thank you again.
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    Re: Finding criteria for a household financial budget falsification

    How can someone who has income of 10,000 ened up with a net budget of 20,000? I assumed that 'R' - whch you called "the investigated net budget" is the true results, and that 'P' is the results as reported by the household. If you define 'I' to be the household's "true" income then 'I' must be greater than 'R'.

    Perhaps I don't understand how R and P are defined. In your original post you wrote this: "Suppose that householdsí net budget is P and our investigated outcome of net budget is R. As you know: R>=P." Please explain what you mean by "investigated outcome of net budget" and why R>=P. Thanks.
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    Re: Finding criteria for a household financial budget falsification

    Quote Originally Posted by ebaines View Post
    How can someone who has income of 10,000 ened up with a net budget of 20,000? I assumed that 'R' - whch you called "the investigated net budget" is the true results, and that 'P' is the results as reported by the household. If you define 'I' to be the household's "true" income then 'I' must be greater than 'R'.

    Perhaps I don't understand how R and P are defined. In your original post you wrote this: "Suppose that households’ net budget is P and our investigated outcome of net budget is R. As you know: R>=P." Please explain what you mean by "investigated outcome of net budget" and why R>=P. Thanks.
    I , E and P=I-E (proposed net budget) are the values that households are declaring. Maybe in some cases all of these items are false. So we investigate and find a true R (real net budget). So now we can Have this condition I mentioned in previous post :

    I=10,000 E=1000 P=9,000 R=20,000 so we have : |(R-P)/I|=1.1

    A household has 10,000 income, and 1000 expense so the proposed net budget is 9,000 . So after they declare these value, we check and find true 20,000 net budget. Now in all cases we have R>=P .

    Maybe in some other cases we have these situations :
    I=10,000 E=9,000 P=1,000 R=2,000
    or
    I=5,000 E=10,000 P=-5,000 R=2,000
    or
    I=5,000 E=10,000 P=-5,000 R=-2,000
    or
    I=5,000 E=5,000 P=0 R=2,000
    or
    I=-5,000 E=10,000 P=-5,000 R=0 (very rare)

    We can have these conditions and more...

    Thanks.
    Last edited by jacks12; June 10th 2014 at 09:28 AM.
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