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A Diffusion Equation for the Density of the Ratio of Two Jointly Distributed Gaussian Variables and the Exponential Analysis Problem

2012; Society for Industrial and Applied Mathematics; Volume: 34; Issue: 2 Linguagem: Inglês

10.1137/110835323

1095-7197

Piero Barone,

Bayesian Methods and Mixture Models

It is shown that the density of the ratio of two random variables with the same variance and joint Gaussian density satisfies a non stationary diffusion equation. Implications of this result for kernel density estimation of the condensed density of the generalized eigenvalues of a random matrix pencil useful for the numerical inversion of the Laplace transform is discussed.