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I need to estimate a truncated gamma distribution parameters (shape , scale).

But, I only know the data mean and std. dev. I do not know the data set.

Given the mean and std. dev. of a data set from a truncated gamma distribution, how to find shape and scale of the distribution parameters ?

I know MLE may be useful for solving this problem. But, they depend on knowing the whole data set.

Any help would be appreciated.

Brian Tompsett - 汤莱恩
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user3356689
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1 Answers1

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Well, there are probably some expressions for the mean and variance of a truncated gamma distribution. You can solve the equations for (truncated gamma mean) = (observed mean) and (truncated gamma variance) = (observed variance). A difficulty is that the truncated distribution has an extra free parameter, namely the cut-off point. There are probably many combinations (maybe a continuous set) of parameters including the cut-off point which fit the observed mean and variance, so you will have to introduce some criterion for selecting one combination in that set. E.g. make the cut-off point as small or as large as possible. Maybe you have some information about the cut-off point that you can bring to bear. Good luck.

Robert Dodier
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  • the "cut-off point" is the truncated point ? If yes, they are known. But, how to get the distribution parameters from the observed mean and variance ? Thanks ! – user3356689 Mar 19 '14 at 13:36