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Unified extension of variance bounds for integrated Pearson family

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  • Giorgos Afendras

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

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  • Giorgos Afendras, 2013. "Unified extension of variance bounds for integrated Pearson family," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(4), pages 687-702, August.
    • Handle: RePEc:spr:aistmt:v:65:y:2013:i:4:p:687-702
    DOI: 10.1007/s10463-012-0388-3
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    References listed on IDEAS

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    1. V. Papathanasiou, 1995. "A characterization of the Pearson system of distributions and the associated orthogonal polynomials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(1), pages 171-176, January.
    2. Wei, Zhengyuan & Zhang, Xinsheng, 2009. "Covariance matrix inequalities for functions of Beta random variables," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 873-879, April.
    3. Cacoullos, T. & Papathanasiou, V., 1985. "On upper bounds for the variance of functions of random variables," Statistics & Probability Letters, Elsevier, vol. 3(4), pages 175-184, July.
    4. Chen, Louis H. Y., 1982. "An inequality for the multivariate normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 12(2), pages 306-315, June.
    5. R. Korwar, 1991. "On characterizations of distributions by mean absolute deviation and variance bounds," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(2), pages 287-295, June.
    6. Papathanasiou, V., 1988. "Variance bounds by a generalization of the Cauchy-Schwarz inequality," Statistics & Probability Letters, Elsevier, vol. 7(1), pages 29-33, July.
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    1. Giorgos Afendras & Vassilis Papathanasiou, 2014. "A note on a variance bound for the multinomial and the negative multinomial distribution," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(3), pages 179-183, April.

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