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On a ranking problem for symmetric and unimodal location parameter families

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  • Roters, M.

Abstract

Consider a location family of distributions generated by a symmetric and unimodal density w.r.t. Lebesgue measure. In this paper we prove that the probability of correctly ranking k = 3 populations from the above class of distributions subject to the condition that the range of the location parameters is bounded by 2[delta] is maximized for the parameter configuration (0, [delta], 2[delta]). The corresponding conjecture that for k [greater-or-equal, slanted] 4 this maximum is also attained for the 'equally spaced means configuration' as above has, in general, a negative answer. A counterexample is given for k = 4 in the normal case.

Suggested Citation

  • Roters, M., 1993. "On a ranking problem for symmetric and unimodal location parameter families," Statistics & Probability Letters, Elsevier, vol. 16(1), pages 47-49, January.
    • Handle: RePEc:eee:stapro:v:16:y:1993:i:1:p:47-49
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