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Don't know if a solution is possible. Real world problem.

  1. Mar 22, 2012 #1
    How would you find/estimate the probability of receiving the same utility bill, to the cent, two months in a row. This is a continuous distribution with an infinite amount of solution. However, for practicality, I want to make the distribution more finite. In reality, my bill will probably never exceed 150. I won't be able to tell you the mean or median of the distribution, but a very rough estimate of the interquartile range is $40-80.


  2. jcsd
  3. Mar 23, 2012 #2


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    Hey trueacoustics and welcome to the forums.

    Although this might seem like a simple question, it isn't.

    The thing for this is to figure out how past bills and usage affects your new bill. If you assume that both bills are independent, then the problem is made much easier. If you assume that your past bill only depends on factors that relate to the previous one, it makes things a little more complex, but still manageable.

    The point is you need to first figure out what will affect your bill both on any past data as well as things that don't necessarily relate to the data of your past bills.

    Here is a good way to think about this: you could take all your bill data for the past two years and draw some kind of graph. That graph might tell you something useful, but it won't tell you the most important things.

    For example you might find that for certain months, you need to use more water, more heating and so on. Now you might argue that this would be reflected in the price of your bill at certain points.

    But what for example your electricity company introduces off-peak hours where they charge you significantly less for using power in those times? If you know this then you will pick this out but if you were not aware of this fact you wouldn't know what to think.

    So the first thing you need to do is firstly think about what affects your power prices. Does the time of year affect it? What about the day of the week? What about where you live? Does any changes in lifestyle have an impact? (You might be away from home some part of the year)

    The point I'm trying to make is not to just think of the data for bill prices because that really in the grand scheme of things doesn't tell you much: if you understand how your actions contribute to the final bill you get each month then you will understand more or less how it is calculated on those principles.

    But let's just for the moment say that for your example, that each month is modelling by a normal distribution with mean = m and variance = v and each month is independent from the next.

    Basically you will have an interval for your bill price so lets say your interval is [b-d,b+d] where d is some kind of noise correction (for your example I'd make it 2 cents) and b is your bill price.

    Then using this you need to calculate P(b - d < A < b + d) x P(b - d < B < b + d) which can be found if you standardize the values based on (m,v) and then use a computer.

    But I really really have to stress: this is so simplifying that it's probably useless in a practical sense.

    It's the same kind of reason that looking purely at stock price history data is dangerous if you want to actually do serious investing especially if you don't understand anything about how markets work, how things are valued, how to assess a business model and how it makes money and so on.
  4. Mar 23, 2012 #3
    I never assumed it was simple. That's why I said I don't even know if it could be solved. There are a very large amount of variables which go into the equation, and I won't be able to account for most of them. I think the variable which I really want to consider are these facts, and the rest can be assumed nonexistent:
    Three people living in the apartment
    10 appliances which produce water
    13 appliances that produce electricity
    I am just trying to get a very rough estimate.

    Everything else is extremely variable and improvable to consider.


  5. Mar 23, 2012 #4


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    If you think that the use for each month will be modelled by the same distribution and the months are independent then you can use the formula P(A and B) = P(A)P(B) where P(A) is the probability of getting a price range for month A and P(B) is the probability of getting the same price for the next month B.

    What you could do is take your past data and get an estimate for your mean and variance and then for your price get the probability based on these estimated parameters.

    But I have to ask in what context is this being used? If it's been used in any serious capacity then my advice would be not to use this. If it is just for interest and not to be used for serious decision making then I guess no harm can be done.

    The point is if you want to use this for something serious, then it's not a good idea to use the above model. If you want to do this it's probably better if you look at the past bills and think about the usage in terms of what appliances you use and what your friends use over given periods and then get some rule of thumb measure. Certainly the normal distribution is a good way to approximate things like this, but yeah you have to be careful.
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