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## Main Question or Discussion Point

Hi, I am doing research and I am stuck at this point I need help to convolute iid non central chi-square with normal distribution.

- Thread starter mmmly2002
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Hi, I am doing research and I am stuck at this point I need help to convolute iid non central chi-square with normal distribution.

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chiro

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Can you elaborate on what part you are stuck on? Have you set up the convolution equation? What approaches have you tried? Straight convolution? MGF approach?

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Thanks again for your help.

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chiro

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If so what I recommend is to get the MGF by multiplying the two MGF's (assuming they are independent) and then using the characteristic function for your combined MGF to get the PDF.

Also don't rule out using a term by term integration as opposed to doing something analytically.

If the analytic distribution is extremely complicated and can't easily be expressed with the elementary functions, then what you can do is basically look at the order of the expanding taylor series centred about some point and then cut off the series when the error term (in terms of its order) is large enough.

If you want to do strict calculations, then get an approximation with the right error properties over the domain of the PDF and use that.

You should be able to pick enough terms to reduce the order and you can program a computer to calculate the first n terms and throw them in an array.

But if you use an approximated PDF, make sure you "re-normalize" it so that it has the proper properties of a PDF.

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