## Abstract

Let X={X_{(1)},X_{(2)},⃛, X_{(n)}} a collection of real numbers, ordered from smallest to largest. In this paper we consider the problem of Finding the weighted kth smallest element of the multiset X + X= {X_{(i)} + X_{(j)}:1≦ i≦ j ≦n}, in which X_{(i)} + X_{(j)}has weight w(i, j) = a(j-i+1) — a(j-i), where 0 = a(0)≦a(l)≦ ⃛ ≦a(n)≠0 are a set of integers called scores. We derive relations involving the weights w(i,j) which can in principle be used to eliminate a number of elements of X+X which cannot possibly be the kth smallest, regardless of the distribution of X. These results are applied to Wilcoxon scores and to winsorized Wilcoxon scores. We describe a fast algorithm for finding the weighted kth smallest element in both cases.

Original language | English |
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Pages (from-to) | 19-35 |

Number of pages | 17 |

Journal | Journal of Statistical Computation and Simulation |

Volume | 31 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1989 |

## ASJC Scopus subject areas

- Statistics and Probability
- Modeling and Simulation
- Statistics, Probability and Uncertainty
- Applied Mathematics