Suppose I have a vector of random variables $\mathbf{X}$ whose pdf is given by a multivariate Gaussian $\mathcal{N}(\boldsymbol{\mu}, \boldsymbol{\Sigma})$. What is the pdf for the joint distribution of the element-wise square of the random variable, i.e. $\mathbf{X}\odot\mathbf{X}$, where $\odot$ is the Hadamard product?
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Would you be satisfied with formulas for its characteristic or moment generating functions? – kimchi lover Nov 13 '17 at 19:07
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Moment generating function might work. – user2452976 Nov 13 '17 at 19:51