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

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 ...

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 ...

D. O. Loftsgaarden, C. P. Quesenberry, A Nonparametric Estimate of a Multivariate Density Function, The Annals of Mathematical Statistics, Vol. 36, No. 3 (Jun., 1965 ...

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 ...