Weighted quantile correlation test for the logistic family

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We summarize the results of investigating the asymptotic behavior of the weighted quantile correlation tests for the location-scale family associated to the logistic distribution. Explicit representations of the limiting distribution are given in terms of integrals of weighted Brownian bridges or alternatively as infinite series of independent Gaussian random variables. The power of this test and the test for the location logistic family against some alternatives are demonstrated by numerical simulations.