Bivariate extension of the method of polynomials for Bonferroni-type inequalities
type: Item
instance of: scholarly article
title: Bivariate extension of the method of polynomials for Bonferroni-type inequalities
zbMATH Open document ID: 0817.60011
author: Yuan Xu
author: Janos Galambos
published in: Journal of Multivariate Analysis
publication date: 1995-03-16T00:00:00Z
review text: The classical Bonferroni inequality is well-known. With the help of method of inclusion and exclusion a number of generalisations of this inequality were obtained [see, for example, \textit{R. M. Meyer}, Ann. Math. Stat. 40, 692-693 (1969; Zbl 0175.472)]. A special class of Bonferroni- type inequalities, so called bivariate inequalities, attracts attention. In recent joint publications (1992-1994) of the authors and M. Y. Lee there were obtained some bivariate inequalities by means of the method of polynomials, which in the univariate case is due to the first author and \textit{R. Mucci} [Publ. Math. 27, 263-268 (1980; Zbl 0455.60014)]. The authors of the present paper stress that their method of polynomials ``is not merely a method for proving inequalities but rather its real value is in the generation of new inequalities''. They illustrate their method by proving some new bivariate inequalities.
Mathematics Subject Classification ID: 60E15
zbMATH DE Number: 718687
zbMATH Keywords: Bonferroni inequality
zbMATH Keywords: bivariate inequalities
MaRDI profile type: Publication
full work available at URL: jmva.1995.1007
OpenAlex ID: W2004876947
DOI: 10.1006/JMVA.1995.1007
description: scientific article; zbMATH DE number 718687