Parzen Window Density Estimation

This well-know non-parametric scheme directly uses the samples drawn from an unknown distribution to model its density. The general form of the density is then:

        P^*(x,a) = 1/N \Sum_i{ R(x - x_i) }

Where:

        a = { x₀, x₁, ... , x_N-1 },
and

         R is the smoothing function


The choice of R is important since it's conditionning the quality of the estimate. The
most popular function is the gaussian distribution, and we've choosen it because it's
easy to manipulate and derive. The choice of the variance is then very important as
well, but in our implementation, this parameter is optimized over the iterations.