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I am a bit confused about calculating the third zero-centred statistical moment for the function f=X/Y (X and Y are normal distributions), assuming I can calculate the third and all the lower mean- and zero-centred X and Y moments. Am I wrong in imagining it would be a formula similar to the uncertainty propagation one, only for higher moments? I don't know where to start

Francesco
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  • If $X$ and $Y$ are random variables, the short answer is you can't perform this calculation in general with just the information you specify. If $X$ and $Y$ really are "distributions," then please tell us what you mean by their ratio. If they really are "random distributions," which means they are selected randomly from some set of distributions, then please tell us how that is done. – whuber Nov 07 '22 at 02:33
  • OK, let's assume $X$ and $Y$ are normal distributions – Francesco Nov 07 '22 at 08:29
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    Assuming $X$ and $Y$ are random variables, the third moment of that ratio is undefined: see https://stats.stackexchange.com/a/299765/919. – whuber Nov 07 '22 at 13:22

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