Density
estimation is one of the most important and difficult statistical problems.
There exists a vast literature on the topic and this is not the goal of the paper to provide an overview of all existing approaches. Mainly three
methodologies have been developed: First, a non parametric approach can be used,
such as kernel density estimation, penalized maximum likelihood or spline
density smoothing. Second, finite mixture can be applied to model multi model
distributions. Third, polynomials can be used for the log density modelling and
estimation. The latter approach, taken in the present paper, is the simplest
and can be used at a preliminary stage of density estimation.
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