  Given two sets of training samples, general method is to estimate the density
function and classify the test sample according to higher values of estimated
densities. Natural way to estimate the density should be histogram tending to
frequency curve. But nature of different amount of data accumulation at
different points, obstruct us to take common interval length in drawing
histogram. Here we followed a method similar to drawing histogram with an
intention to density estimation and classification, but without doing
arbitrarily we considered diagram of the scattered plot and has obtained
estimate of density based on areas of the Voronoi cells. But area of arbitrary
Voronoi cell may be difficult to find out particularly in two and higher
dimensions, and also in manifolds. For this reason we estimate the area of the
Voronoi cell by drawing many independent uniform variates covering the support
of the training samples. Please note that though we have in mind density
estimation and classification problem in higher dimension and in typical
manifolds, but our simulations and algebraic calculations have been mostly
shown for densities on real line. We expect in higher dimension and in
manifolds the work will be in similar lines and plan to do in near future. Also
we expect discrete cases can be handled in slightly different but similar lines
which are also left for future works.
