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The angular central Gaussian distribution (ACG) is the distribution of $\frac{\mathbf{x}}{\|\mathbf{x}\|}$, when $\mathbf{x}\sim\mathcal{N}\left(\boldsymbol{0},\mathbf{A}\right)$, where $\mathbf{x}$ is a $p$-dimensional vector and $\mathbf{A}$ is a positive definite matrix.

Is there a distribution for $\frac{\mathbf{x}}{\|\mathbf{x}\|}$, when $\mathbf{x}\sim\mathcal{N}\left(\boldsymbol{\mu},\sigma\mathbf{I}\right)$, where $\boldsymbol{\mu}$ is the mean vector (non-zero) and $\mathbf{I}$ is the identity matrix?

Thanks, Corina

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