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

• Autorzy: G. Afendras , N. Papadatos
• Języki publikacji: 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.

Kategorie tematyczne

• 62E15: Exact distribution theory
• 62-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
• 60E05: Distributions: general theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2015
• Tom: 42
• Numer: 2-3
• Strony: 231-267

Daty

wydano

2015

Twórcy

autor

G. Afendras

• Department of Biostatistics, University at Buffalo, Buffalo, NY 14214, U.S.A.

autor

N. Papadatos

• Department of Mathematics, Section of Statistics and O.R., University of Athens, Panepistemiopolis, 157 84 Athens, Greece

Identyfikatory

DOI

10.4064/am42-2-9