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

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 ...

Nonparametric method for multivariate density estimation using neural networks In this paper, a parameter-free method is proposed to determine the probability density function of multi-dimensional ...