Geodesic
Integrated Pearson family and orthogonality of the Rodrigues polynomials: A review including new results and an alternative classification of the Pearson system
G. Afendras 1   ; N. Papadatos 2
1 Department of Biostatistics University at Buffalo Buffalo, NY 14214, U.S.A.
2 Department of Mathematics Section of Statistics and O.R. University of Athens Panepistemiopolis 157 84 Athens, Greece
Applicationes Mathematicae, Tome 42 (2015) no. 2-3, pp. 231-267 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/am42-2-9
Keywords: alternative classification pearson family probability densities related orthogonality corresponding rodrigues polynomials leads subset ordinary pearson system so called integrated pearson family basic properties family discussed reviewed results presented detailed comparison between integrated pearson family ordinary pearson system presented including algorithm enables decide whether given pearson density belongs integrated system recurrences between derivatives corresponding orthonormal polynomials given

G. Afendras  1   ; N. Papadatos  2

1 Department of Biostatistics University at Buffalo Buffalo, NY 14214, U.S.A.
2 Department of Mathematics Section of Statistics and O.R. University of Athens Panepistemiopolis 157 84 Athens, Greece 
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G. Afendras; N. Papadatos. Integrated Pearson family and orthogonality of the Rodrigues polynomials: A review including new results and an alternative classification of the Pearson system. Applicationes Mathematicae, Tome 42 (2015) no. 2-3, pp. 231-267. doi: 10.4064/am42-2-9

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