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We study nonparametric estimation of the distribution function (DF) of acontinuous random variable based on a ranked set sampling design using theexponentially tilted (ET) empirical likelihood method. We propose ET estimatorsof the DF and use them to construct new resampling algorithms for unbalancedranked set samples. We explore the properties of the proposed algorithms. For ahypothesis testing problem about the underlying population mean, we show thatthe bootstrap tests based on the ET estimators of the DF are asymptoticallynormal and exhibit a small bias of order $O(n^{-1})$. We illustrate the methodsand evaluate the finite sample performance of the algorithms under both perfectand imperfect ranking schemes using a real data set and several Monte Carlosimulation studies. We compare the performance of the test statistics based onthe ET estimators with those based on the empirical likelihood estimators.

Exponentially Titled Empirical Distribution Function for Ranked Set Samples