A New Simulation Algorithm for Estimating Non-differentiable Probability Density Functions
Yihan Luo · Jisuanji fangzhen · 2008
A new and effective simulation algorithm is proposed to estimate the probability density function (PDF) of a series of observations, which can even identify the non-differentiable points of the PDF and correct the errors in the neighborhoods. The algorithm contributes to many fields such as entropy estimation, independence analysis, blind signal process and so on. It includes 5 steps: empirical cumulative distribution function (ECDF) calculation, ECDF re-sampling, ECDF smoothing, non-differentiable points correction and PDF calculation. Thereinto, a new algorithm called Centroid Seeking in Every Three Points is used to do the third step. And, a new identification algorithm, three identification rules and a new correction algorithm are used for the fourth step of correction. The algorithm overcomes the difficulty of estimating non-differentiable PDFs which the old methods hardly do, and makes the errors much less. Finally, computer simulation proves its effectivity and practicability.