On a ranking problem for symmetric and unimodal location parameter families
Identifieur interne : 000457 ( Istex/Corpus ); précédent : 000456; suivant : 000458On a ranking problem for symmetric and unimodal location parameter families
Auteurs : M. RotersSource :
- Statistics and Probability Letters [ 0167-7152 ] ; 1993.
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 2δ is maximized for the parameter configuration (0, δ, 2δ). The corresponding conjecture that for k ⩾ 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.
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DOI: 10.1016/0167-7152(93)90121-X
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