Estimation of density functions and upcrossing-rates from samples

This paper assesses techniques for estimating univariate probability density functions, and highlights strengths and weaknesses of several methods. Applications are given for non-Gaussian distributions typical of the dynamic response of nonlinear systems. It is concluded that of the methods considered the maximum likelihood method is generally the most suitable when predicting extreme values. The moment and maximum likelihood methods are adapted for estimation of upcrossing-rate functions.