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

Let X 1, X 2, ⋯ be independent identically distributed random variables having a common probability density function f. After a so-called kernel class of estimates f n of f based on X 1, ⋯, X n was ...

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

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 ...