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 simple transformations ...

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 ...

Fundamental methods are developed for the derivation of the probability density function and moments of rational algebraic functions of independent random variables. Laplace and Mellin integral ...

Example of the Hazard Rate The probability density calculates the probability of failure at any given time. For instance, a person is certain to die eventually.

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 ...

Kernel Density Estimation (KDE): A nonparametric method to estimate the probability density function of a random variable by averaging over locally weighted contributions of each data point.