Region of maximum probability content of fixed diameter

R.n Rattihalli

Journal of Multivariate Analysis, 1990, vol. 32, issue 2, 290-295

Abstract: In this article it is shown that when the pdff(x) is non-increasing in xi, i = 1, 2, ..., k, the sphere of diameter d centred at the origin has largest probability content as compared to any other region of diameter at most d. As a consequence, it follows that a sphere of diameter d has largest volume among the regions of diameter at most d. Further, the results are used to obtain certain optimum statistical decision rules.

Keywords: diameter; probability; density; function; convex; set (search for similar items in EconPapers)
Date: 1990
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