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.

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 ...

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 ...

Both normality and lognormality appear to be exceptions rather than the rule with respect to those distributions that may properly be inferred from the stochastic properties of the several series. The ...