Distributions determined by conditioning on a pair of order statistics |
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| Authors: | K Balasubramanian M I Beg |
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| Institution: | 1. Indian Statistical Institute, Delhi Centre, 7 S.J.S. Sansanwal Marg, 110016, New Delhi, India
2. School of Mathematics, University of Hyderabad, 500134, Hyderabad, India
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| Abstract: | LetX
1,X
2, ...,X
n
(n≥3) be a random sample on a random variableX with distribution functionF having a unique continuous inverseF
−1 over (a,b), −∞≤a<b≤∞ the support ofF. LetX
1:n
<X
2:n
<...<X
n:n
be the corresponding order statistics. Letg be a nonconstant continuous function over (a,b). Then for some functionG over (a, b) and for some positive integersr ands, 1<r+1<s≤n
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