2026-07-09http://hdl.handle.net/123456789/540863Often analysts must conduct risk analysis based on a small number of observations. This paper describes and illustrates the use of a kernel density estimation procedure to smooth out irregularities in such a sparse data set for simulating univariate and multivariate probability distributions.Simulating Multivariate Distributions with Sparse Data: A Kernal Density Smoothing ProcedureText