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

G. Afendras, and 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 42.2-3 (2015): 231-267. <http://eudml.org/doc/279995>.

@article{G2015,
abstract = {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.},
author = {G. Afendras, N. Papadatos},
journal = {Applicationes Mathematicae},
keywords = {integrated Pearson family of distributions; derivatives of orthogonal polynomials; Rodrigues polynomials},
language = {eng},
number = {2-3},
pages = {231-267},
title = {Integrated Pearson family and orthogonality of the Rodrigues polynomials: A review including new results and an alternative classification of the Pearson system},
url = {http://eudml.org/doc/279995},
volume = {42},
year = {2015},
}

TY - JOUR
AU - G. Afendras
AU - N. Papadatos
TI - Integrated Pearson family and orthogonality of the Rodrigues polynomials: A review including new results and an alternative classification of the Pearson system
JO - Applicationes Mathematicae
PY - 2015
VL - 42
IS - 2-3
SP - 231
EP - 267
AB - 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.
LA - eng
KW - integrated Pearson family of distributions; derivatives of orthogonal polynomials; Rodrigues polynomials
UR - http://eudml.org/doc/279995
ER -