Estimating probability densities from short samples: a parametric maximum likelihood approach

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Abstract
A parametric method similar to autoregressive spectral estimators is proposed to determine the probability density function (pdf) of a random set. The method proceeds by maximizing the likelihood of the pdf, yielding estimates that perform equally well in the tails as in the bulk of the distribution. It is therefore well suited for the analysis short sets drawn from smooth pdfs and stands out by the simplicity of its computational scheme. Its advantages and limitations are discussed.

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