Unified extension of variance bounds for integrated Pearson family

Giorgos Afendras ()

Annals of the Institute of Statistical Mathematics, 2013, vol. 65, issue 4, 687-702

Abstract: We use some properties of orthogonal polynomials to provide a class of upper/lower variance bounds for a function $$g(X)$$ of an absolutely continuous random variable $$X$$ , in terms of the derivatives of $$g$$ up to some order. The new bounds are better than the existing ones. Copyright The Institute of Statistical Mathematics, Tokyo 2013

Keywords: Completeness; Derivatives of higher order; Fourier coefficients; Orthogonal polynomials; Parseval identity; Pearson family of distributions; Rodrigues-type formula; Variance bounds (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10463-012-0388-3

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