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 ...

Leonard Fortuin, Five Popular Probability Density Functions: A Comparison in the Field of Stock-Control Models, The Journal of the Operational Research Society, Vol. 31, No. 10 (Oct., 1980), pp.