Large sample estimation of the mean and the standard deviation of the logistic distribution is discussed. Best linear unbiased estimates based on k = 2(1)9 sample quantiles are used. The optimum spacings, the coefficients to be used in computing the estimates and the variances and asymptotic efficiencies of the estimates are given. A comparison is obtained between the optimum spacings and spacing the observations using the expected values of order statistics.
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Khatab M. Hassanein (1969) studied this question.