Manifestly positive series approximation to probability densities

摘要

When one expands a probability density in a series and truncates the series, the result is generallynot a manifestly positive density. Such is the case, for example, in the classical Edgeworth andGram-Charlier series. In contrast, in quantum mechanics, approximation methods always retainthe manifestly positive aspect of a probability density. We explore this fundamental difference andattempt to modify standard probability theory using the methods of quantum mechanics so thatexpansions result in a manifestly positive probability density.