Thek-th Largest Coordinate of an Orderedn-tuple
Richard M. Meyer · The American Statistician · 1969
In [1] is found the statement given an ordered ntuple (x1,x2, .. ,xn) of real nuinbers, we inay reorder it in increasing order of magnitude to obtain a new nt-tuple (x(l),x(2), X(n)) Withl X(i) ?< X(2) < ... < X(n). This operation applied to all points of the space RI' induces a well-defined function. . If the original n-tuple represents the items of a sample, then the new n--tuple represents the so-called ordered sample. A recursive formula exists for the k-th coordinate of the new n-tuple in terms of the coordinates of the original n-tuple. Expanding the notation above, let X'11(j) (xi,. Jm) (j = l n) denote the j-th (in nondecreasing order) among the real numbers (xil ,x.im) We have for sample size i7 = 2 that X2 XI~~ x+ X2 lXI -X2,(1 X(i) (x1,x2) -mil (x,lx2) 2 2 2 (l)