Corpus ID: 88515886

Representation for the Gauss-Laplace Transmutation

  title={Representation for the Gauss-Laplace Transmutation},
  author={Peng Ding and Joseph K. Blitzstein},
  journal={arXiv: Statistics Theory},
Under certain conditions, a symmetric unimodal continuous random variable $\xi$ can be represented as a scale mixture of the standard Normal distribution $Z$, i.e., $\xi = \sqrt{W} Z$, where the mixing distribution $W$ is independent of $Z.$ It is well known that if the mixing distribution is inverse Gamma, then $\xi$ is student's $t$ distribution. However, it is less well known that if the mixing distribution is Gamma, then $\xi$ is a Laplace distribution. Several existing proofs of the latter… Expand
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