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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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    How could I do this parameter estimation?2012-05-28

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Following on what Ilya commented, you can look at the history and try to model the distribution. Certainly you can take a mean and standard deviation and make a Gaussian. But there are many other things to think about. Maybe all payments are a multiple of $\$1 or \$100$. Do you expect that to continue? It seems that an arbitrary payment of $\$0$ is always possible-somebody can forget, but an arbitrary payment of $\$1$ is much less likely if all previous have been of order $\$1000$. The Gaussian distribution almost always has smaller tails than real-world cases.

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    @angaran: I like Numerical Recipes http://apps.nrbook.com/c/index.html Obsolete versions are free. Any numerical analysis text should have a section.2012-05-30