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hypothesis of randomness; two-sample location-scale problem; quadratic forms of linear rank statistics; asymptotically independent; contiguous alternatives; asymptotic power; alternatives of difference in location and scale; score generating function
The equivalence of the symmetry of density of the distribution of observations and the oddness and evenness of the score-generating functions for the location and the scale problem, respectively, is established at first. Then, it is shown that the linear rank statistics with scores generated by these functions are asymptotically independent under the hypothesis of randomness as well as under contiguous alternatives in the last part of the paper. The linear and quadratic forms of these statistics are considered for testing the two-sample location-scale problem simultaneously.
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