Abstract
A new derivation of the classical orthogonal polynomials is given by using thew-function which appears in the variance bounds and some properties of the Pearson system of distributions. Also a characterization of the Pearson system of distributions through some conditional moments is obtained by using a result obtained by Johnson (1993) concerning this family.
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Papathanasiou, V. A characterization of the Pearson system of distributions and the associated orthogonal polynomials. Ann Inst Stat Math 47, 171–176 (1995). https://doi.org/10.1007/BF00773421
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DOI: https://doi.org/10.1007/BF00773421