# Wydawnictwa / Czasopisma IMPAN / Applicationes Mathematicae / Wszystkie zeszyty

## Applicationes Mathematicae

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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

### Tom 42 / 2015

Applicationes Mathematicae 42 (2015), 231-267 MSC: Primary 62E15, 60E05; Secondary 62-00. DOI: 10.4064/am42-2-9

#### Streszczenie

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.

#### Autorzy

• G. AfendrasDepartment of Biostatistics
University at Buffalo
Buffalo, NY 14214, U.S.A.
e-mail