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Recently, MiniMax ranked set sampling (MiniMax RSS) scheme is suggested for population mean estimation. In this article, we consider moving extreme ranked set sampling (MERSS) and MiniMax RSS for estimating the distribution function of a random variable. Using the maximum likelihood estimation method, new estimators of the cumulative distribution function (CDF) are derived and also their variances are obtained. In the light of a simulation study, we conclude that the estimators based on MiniMax RSS work well compared to those based on MERSS setups regardless of the ranking quality. Additionally, the proposed concomitant-based CDF estimators tend to be superior to their analogs as long as the ranking process is done with fairly good accuracy. For the sake of illustration, two empirical datasets are considered to show the applicability of the proposed estimators in practice.

Estimation of the distribution function using moving extreme and MiniMax ranked set sampling