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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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Afendras G., Papadatos N.

Applicationes Mathematicae

2015

tom 42

nr 2-3

231-267

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.

Ograniczanie wyników

1 Applicationes Mathematicae

1 Afendras G.

1 Papadatos N.

1 2015

Wyniki wyszukiwania

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