Abstract:
Let Z be a standard Gaussian random variable, X be independent of Z, and t be a strictly positive scalar. For the derivatives in t of the differential entropy of X+√tZ, M...Show MoreMetadata
Abstract:
Let Z be a standard Gaussian random variable, X be independent of Z, and t be a strictly positive scalar. For the derivatives in t of the differential entropy of X+√tZ, McKean noticed that Gaussian X achieves the extreme for the first and second derivatives, and he conjectured that this holds for general orders of derivatives. Here we show that, when the probability density function of X+√tZ is log-concave, this conjecture holds for orders up to at least five. We also recover Toscani's result on the non-negativity of the third derivative of the entropy power of X+√tZ for log-concave densities, using a much simpler argument.
Date of Conference: 17-22 June 2018
Date Added to IEEE Xplore: 16 August 2018
ISBN Information:
Electronic ISSN: 2157-8117