Use EM algorithm to compute the NPMLE of CDF and also the two censoring distributions. For doubly censored data (as described in Chang and Yang (1987) Ann. Stat. 1536-47). You can also specify a constraint, it will return the constrained NPMLE and the -2 log empirical likelihood ratio. This can be used to test the hypothesis about the constraint and find confidence intervals for probability or quantile via empirical likelihood ratio theorem. Influence function of hat F may also be calculated (but may be slow).