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 ...

Ushio Sumita, Yasushi Masuda, Classes of Probability Density Functions Having Laplace Transforms with Negative Zeros and Poles, Advances in Applied Probability, Vol. 19, No. 3 (Sep., 1987), pp.

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.

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 ...