A probability density function (PDF) describes the likelihood of different outcomes for a continuous random variable.

We propose a method for reconstructing a probability density function (pdf) from a sample of an n -dimensional probability distribution. The method works by iteratively applying simple transformations ...

In some situations only the statistical properties of such objects are desired: the three-dimensional probability density function. This article demonstrates that under special symmetries this ...

Some of the associated probability density functions involve Bessel functions and theta functions. We describe properties of the operators, including how they transform moments.

Building on the widely-used double-lognormal approach by Bahra (1997), this paper presents a multi-lognormal approach with restrictions to extract risk-neutral probability density functions (RNPs) for ...