GENERALIZED PEARSON DISTRIBUTIONS AND RELATED CHARACTERIZATION PROBLEMS

CLAUDE LEFÈVRE^{1}, VASILIS PAPATHANASIOU^{2} AND SERGEY UTEV^{3}

1Institut de Statistique et de Recherche Opérationnelle, C.P.210, Université Libre de Bruxelles,

Boulevard du Triomphe, B-1050 Bruxelles, Belgique, e-mail: clefevre@ulb.ac.be 2Department of Mathematics, University of Athens, Panepistemiopolis, 15784 Athens, Greece,

e-mail: bpapath@cc.uoa.gr

3School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom, e-mail: sergey.utev@nottingham.ac.uk

(Received November 24, 2000; revised September 10, 2001)

Abstract. This paper is concerned with a Rodrigues’ formula for generating new classes of polynomials. The associated density functions belong to the family of generalized Pearson curves, which extends the classical Pearson family. Various properties of these polynomials (degree, orthogonality …) are investigated and then exploited to derive several related results, especially characterizations, in probability.

Key words and phrases: Rodrigues’ formula, generalized Pearson family of curves, orthogonal polynomials, covariance identity, characterizations.