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

Probability density function is a statistical expression defining the likelihood of a series of outcomes for a continuous variable, such as a stock or ETF return.

A class of nonparametric estimators of f(x) based on a set of n observations has been proved by Parzen [1] to be consistent and asymptotically normal subject to certain conditions. Although quite ...

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 ...