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A diffusion equation for the density of the ratio of Gaussian variables and the numerical inversion of Laplace transform
parabolic equations random matrices kernel estimation
2011/3/21
It is shown that the density of the ratio of two Gaussian random variables with the same variance satisfies a non stationary diffusion equation. Implications of this result for kernel density estimati...
Positive-part moments via the Fourier-Laplace transform
positive-part moments characteristic functions Fourier transforms Fourier-Laplace transforms integral representations
2010/3/18
Integral expressions for positive-part moments EXp
+ (p > 0) of random variables X are presented, in terms of the Fourier-Laplace or
Fourier transforms of the distribution of X. A necessary and suff...