Corpus ID: 88515886

Representation for the Gauss-Laplace Transmutation

@article{Ding2015RepresentationFT,
  title={Representation for the Gauss-Laplace Transmutation},
  author={Peng Ding and Joseph K. Blitzstein},
  journal={arXiv: Statistics Theory},
  year={2015}
}
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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References

SHOWING 1-10 OF 15 REFERENCES
Bounds for the Distribution of the Generalized Variance
Let $D_{p,m}$ be the determinant of the sample covariance matrix for $m + p + 1$ observations from a $p$-variate normal population having identity covariance matrix. We give bounds for theExpand
A Characteristic Function Exercise
A heuristic demonstration that Y = X1X2 + X3X4 follows the Laplace or double exponential distribution [i.e., f(Y) = 2 exp(Y )] if the Xi are independently and normally distributed, N(O, 1), was givenExpand
Scale Mixtures of Normal Distributions
SUMMARY This paper presents necessary and sufficient conditions under which a random variable X may be generated as the ratio ZI V where Z and V are independent and Z has a standard normalExpand
LIGHT BULB STATISTICS
Abstract Using the concept of an idealized light bulb, one subject to a constant probability of failure while in use, certain distribution problems are solved heuristically. These include: (1) TheExpand
The Bayesian Lasso
The Lasso estimate for linear regression parameters can be interpreted as a Bayesian posterior mode estimate when the regression parameters have independent Laplace (i.e., double-exponential) priors.Expand
A Stochastic Approach to the Gamma Function
An Introduction to Multivariate Statistical Analysis
TLDR
The introduction to multivariate statistical analysis is universally compatible with any devices to read, and will help you to cope with some harmful bugs inside their desktop computer. Expand
First and Second Laws of Error
(1923). First and Second Laws of Error. Journal of the American Statistical Association: Vol. 18, No. 143, pp. 841-851.
The Laplace distribution and 2 × 2 unit normal determinants
  • The American Statistician
  • 1987
Pitman measure of closeness
  • The American Statistician
  • 1986
...
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2
...