Consider independent observations (X_1,R_1), (X_2,R_2), ..., (X_n,R_n) with random or fixed ranks R_i in {1,2,...,m}, while conditional on R_i = k, the random variable X_i has the same distribution as the k-th order statistic within a random sample of size m from an unknown continuous distribution function F. Such observation schemes are utilized in situations in which ranking observations is much easier than obtaining their precise values. Two wellknown special cases are ranked set sampling (McIntyre 1952) with m = n and R_i = i, and judgement post-stratification (MacEachern et al. 2004} with R_i being uniformly distributed on {1,2,...,m}. One goal is to compute pointwise confidence intervals for the distribution function F with guaranteed coverage probability for finite sample sizes. We propose a solution for this tasks which is based on the conditional distribution of the naive empirical distribution function, given the ranks R_1, R_2, ..., R_n. This procedure motivates a new estimator for the whole distribution function F. Within the setting of judgement post-stratification we analyze and compare the asymptotic distribution of the new estimator, the stratified estimator of Stokes and Sager (1988) and the nonparametric maximum-likelihood estimator of Kvam and Samaniego (1994). It turns out that the former two estimators are asymptotically equivalent, and that the latter estimator is asymptotically more efficient, although the efficiency gain is rather small.