Abstract

First, it is shown that a univariate bona fide density approximation can be obtained by assuming that the derivative of the logarithm of the density function under consideration is expressible as a rational function or a polynomial. Then, the density function of a bivariate continuous random vector is approximated by standardizing it and applying a polynomial adjustment to the product of the density approximants of the marginal distributions. As well, it is explained that this approach can easily be extended to the estimation of  density functions. For illustrative purposes, the proposed methodology is applied to several datasets. Since this technique is solely based on sample moments, it readily lends itself to the modeling of large datasets.

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