A probability density function, also known as a bell curve, is a fundamental statistics concept, that describes the likelihood of a continuous random variable taking on a specific value.

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 ...

The problem of estimating a probability density function has only recently begun to receive attention in the literature. Several authors [Rosenblatt (1956), Whittle (1958), Parzen (1962), and Watson ...

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 some simple ...

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 ...