Replacing Histogram with Smooth Empirical Probability Density Function Estimated by K-Moments

Abstract

Whilst several methods exist to provide sample estimates of the probability distribution function at several points, for the probability density of continuous stochastic variables, only a gross representation through the histogram is typically used. It is shown that the newly introduced concept of knowable moments (K-moments) can provide smooth empirical representations of the distribution function, which in turn can yield point and interval estimates of the density function at a large number of points or even at any arbitrary point within the range of the available observations. The proposed framework is simple to apply and is illustrated with several applications for a variety of distribution functions.