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 ...

Nonparametric methods provide a flexible framework for estimating the probability density function of random variables without imposing a strict parametric model. By relying directly on observed ...

Geographical and seasonal variations of homogeneity, skewness, and kurtosis of probability density functions (PDFs) of LWP are discussed, in addition to cloud amount. It is clear that not only cloud ...

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 ...