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I have a set of numbers (each one corresponding to a payment made from the same person) and I would like to assign a probability value to a new specified number given that historical data.

I've looked at the Chebyshev's inequality as a simple means to do that but I don't get the expected results. The formula evidences only obvious differences from the time series and also gives too little probability value to numbers that are lower than at least one of the historical ones.

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    You have to construct an underlying model (even if you assume payments do be independent and follow the same distribution, you already build up a model) maybe estimate parameters of the model (if there any) from the history - and then the question can be answered.2012-05-25
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    How could I do this parameter estimation?2012-05-28

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