Parzen Window Estimated Value Convergence of Density Function

Many commonly known density functions can seldom fit the probability density function in real-world problems.In recent years,many researchers attempt to solve these difficulties. This article embarks from a new kind of point of view, regarding population whose classified symbol probability density function form was not known in advance,making use of various

Communicated by WANG Shi-kun Many commonly known density functions can seldom fit the probability density function in real-world problems. In recent years, many researchers attempt to solve these difficulties. This article embarks from a new kind of point of view, regarding population whose classified symbol probability density function form was not known in advance, making use of various dot densities function mean value in a certain scope to estimated the density function of population, using the Parzen Window Estimate method[21 carries on the exploration of the non-parameter estimation to the density distribution function of population. The article studies the estimation of density function under the condition that only some sample information with classified symbol is known, and the theoretical result of probabilistic characteristics and condition of convergence which the density function estimated value pn（X） must satisfy. The proof of the convergence of estimated value is also given.