A characterization of the Pearson system of distributions and the associated orthogonal polynomials

DOI10.1007/BF00773421zbMath0822.62007MaRDI QIDQ1895446

Yanyan Li

Publication date: 18 October 1995

Published in: Annals of the Institute of Statistical Mathematics (Search for Journal in Brave)

zbMATH Keywords

characterizationclassical orthogonal polynomialsconditional momentsvariance bounds\(w\)-functionPearson system of distributions

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Characterization and structure theory of statistical distributions (62E10)

Related Items (5)

First-order covariance inequalities via Stein's method ⋮ Unified extension of variance bounds for integrated Pearson family ⋮ An extended Stein-type covariance identity for the Pearson family with applications to lower variance bounds ⋮ On rereading Stein's lemma: its intrinsic connection with Cramér-Rao identity and some new identities ⋮ Moment-Based Inference for Pearson's QuadraticqSubfamily of Distributions

Cites Work

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• On upper bounds for the variance of functions of random variables
• Variance bounds by a generalization of the Cauchy-Schwarz inequality
• Characterizations of distributions by variance bounds
• On characterizations of distributions by mean absolute deviation and variance bounds
• Characterization of the Pearson family of distributions

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