Estimators for the central location parameter of a distribution

Estimators for the central location parameter and their properties and assumptions.

Estimator Purpose
Mean Estimate the population mean using the sample mean estimator.
Median Estimate the middle of the distribution using the sample median estimator.
Hodges-Lehmann pseudo-median Estimate the population pseudo-median using the Hodges-Lehman pseudo-median estimator.

The pseudo-median is equivalent to the mean/median when the distribution is symmetric.