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## Main Question or Discussion Point

I was reading that moment generating functions have the property of uniqueness. So just wondering: is there a way to get a probability density function from a moment generating function?

- Thread starter arunma
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I was reading that moment generating functions have the property of uniqueness. So just wondering: is there a way to get a probability density function from a moment generating function?

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mathman

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note: If the mgf exists in a neighborhood around 0 then the characteristic function = mgf(i*t)

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Hello:

I am referring to 'Table of Laplace Transforms' by Roberts&Kaufman. But I cannot seem to get a soln for the following Fourier Transform to retrieve my probability density f(x)

c2 * Integral{e^(iwx) * sinh[sqrt(2w)c1] / sinh[sqrt(2w)pi] dw} = f(x)

where -pi< c1 <=0 and c2 is a constant that scales the integral appropriately so that f(x) is p.d.f. Thanks for your help!

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In general, moment generating functions DO NOT have the property of uniqueness. C.F. s are unique.I was reading that moment generating functions have the property of uniqueness. So just wondering: is there a way to get a probability density function from a moment generating function?

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