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I want to transform the first three moments of a sample X of size N to get a new sample Y with moments ($\mu_Y, \sigma_Y, \nu_Y$). The first two moments can be mapped to the target values using the solution discussed in Transform sample to achieve target mean, skewness, etc

Transforming skewness will probably require a non-linear transformation. Does such a transformation exist? (assuming X is drawn from $\mathbb{R}$ and the transformation is free to change the mean and standard deviation as long as the desired skewness is achieved)

KhanSamnida
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  • The thread you reference answers this question. It shows how to transform one distribution into any other, provided it is mathematically possible. (In particular, every continuous distribution can be transformed into any distribution at all.) – whuber Dec 22 '22 at 21:46
  • Thanks! The accepted answer (in the thread I reference) only gives a transformation for the first two moments and equating quantiles doesn't equate moments. There is no discussion/mention of a transformation which can map skewness (and/or higher moments). – KhanSamnida Dec 22 '22 at 23:00
  • You haven't read the entire answer: see the section referring to "equipercentile equating." – whuber Dec 23 '22 at 14:06

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