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On measures of the distance of a mixture from its parent distribution

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  • Hall, Peter

Abstract

In a previous paper in this Journal, Heyde and Leslie [6] examined moment measures of the distance of a mixture from its parent distribution. They confined their attention to the case where the parent distribution is either normal or exponential, and related the moment measures to the more familiar uniform distance between distributions. In this paper we improve on their results by sharpening one of their inequalities. We then use new techniques to extend their investigation to a larger class of parent distributions.

Suggested Citation

  • Hall, Peter, 1979. "On measures of the distance of a mixture from its parent distribution," Stochastic Processes and their Applications, Elsevier, vol. 8(3), pages 357-365, May.
    • Handle: RePEc:eee:spapps:v:8:y:1979:i:3:p:357-365
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    Cited by:

    1. Fujikoshi, Y. & Ulyanov, V.V. & Shimizu, R., 2005. "L1-norm error bounds for asymptotic expansions of multivariate scale mixtures and their applications to Hotelling's generalized," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 1-19, September.
    2. Ryoichi Shimizu & Yasunori Fujikoshi, 1997. "Sharp Error Bounds for Asymptotic Expansions of the Distribution Functions for Scale Mixtures," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(2), pages 285-297, June.

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