 In particular, median-unbiased estimators exist in cases where mean-unbiased and maximum-likelihood estimators do not exist.They are invariant under one-to-one transformations.There are methods of construction median-unbiased estimators for probability distributions that have monotone likelihood-functions, such as one-parameter exponential families, to ensure that they are optimal (in a sense analogous to minimum-variance property considered for mean-unbiased estimators).