Density Estimation Using Non-Conventional Statistics

Abstract

In this work the use of non-conventional statistics for estimating the probability density function of a given process is investigated. It is well known that the calculation of higher-order statistics, like skewness and kurtosis (which I call C-moments), is very sensitive to the presence of outliers and very dependent on sample size. Recently, the development of L-moments estimators (which are linear combinations of
ordered statistics) had a significant impact on the use of sample statistics to infer probabilities. In contrast to C-moments, L-moments provide more robust and consistent sample estimators. I take advantage of this fact to obtain superior nonparametric pdf estimates via the principle of maximum entropy. The potential use of alternative skewness and kurtosis measures is also explored. The results obtained
from simulation studies are discussed.