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2015 | 42 | 2-3 | 231-267
Tytuł artykułu

Integrated Pearson family and orthogonality of the Rodrigues polynomials: A review including new results and an alternative classification of the Pearson system

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EN
Abstrakty
EN
An alternative classification of the Pearson family of probability densities is related to the orthogonality of the corresponding Rodrigues polynomials. This leads to a subset of the ordinary Pearson system, the so-called Integrated Pearson Family. Basic properties of this family are discussed and reviewed, and some new results are presented. A detailed comparison between the Integrated Pearson Family and the ordinary Pearson system is presented, including an algorithm that enables one to decide whether a given Pearson density belongs, or not, to the integrated system. Recurrences between the derivatives of the corresponding orthonormal polynomials are also given.
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autor
  • Department of Biostatistics, University at Buffalo, Buffalo, NY 14214, U.S.A.
autor
  • Department of Mathematics, Section of Statistics and O.R., University of Athens, Panepistemiopolis, 157 84 Athens, Greece
Bibliografia
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_4064-am42-2-9
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