Let us say that we have sample from the multivariable normal distribution. I would like to understand how is possible to apply a transformation to this sample to produce sample that has the sinh-arcsinh distribution written in following paper: Sinh-Archsinh Distributions

My question is related to previous question: Transformation to increase kurtosis and skewness of normal r.v , except in multivariable case. In previous question there is the inverse transform which takes normal sample and gives sinh-arcsinh sample. Is there equivalent transform to the multivariable sample?

Alternative is to take the multivariable pdf of sinh-arcsinh distribution and get the sample directly from that, but I am curious if it can be done from the multivariable normal sample.


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