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This paper focuses on comparing two nonparametric methods of constructing confidence intervals: the maximum entropy (ME) and the empirical likelihood (EL). The objective is to estimate probability distributions given some moment conditions in the presence of length-biased sampling. Some simulation studies are conducted to indicate ME confidence intervals have better coverage probabilities in comparison with their EL counterparts, when the biased data are contaminated. At the end, the ME and EL methods are applied to analyze a set of real data on elderly residents of a retirement center.

Maximum entropy and empirical likelihood in length-biased setting: a comparison study