A class of probability density estimates can be obtained by penalizing the likelihood by a functional which depends on the roughness of the logarithm of the density. The limiting case of the estimates ...

The notion of probability density for a random function is not as straight-forward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we ...

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 ...