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Convolution of unknown distribution

Posted 10 years ago

I got a problem here:

I measured a distribution, let us call it Z. Now, I know that this distribution Z is a convolution of two different distribution. One of them is Gaussian distribution (G) with a known standard deviation. The other one is a distribution (D) , where the function is known, but we have some free parameters.

So, now I want to find the parameters for the distribution D, which outputs distribution Z best.

Anyone an idea?

Best regards from Germany,
POSTED BY: Michael S
The answer depends on many things. 

What kind of distribution is D? It may or may not be reasonable to compute a symbolic representation of Z, which might affect how I'd go about solving this. 

There are many ways to estimate the parameters of a distribution. These estimators have different properties for different situations.  Do you know what these might be for your situation?

I guess the generic answer to the question is to use Convolve or a numerical equivalent to make a representation of Z.  From there you can use EstimatedDistribution or any related functionality to estimate the parameters. 
POSTED BY: Sean Clarke
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