Estimation
Due to their sensitivity to outliers, the sample extrema cannot reliably be used as estimators unless data is clean – robust alternatives include the first and last deciles.
However, with clean data or in theoretical settings, they can sometimes prove very good estimators, particularly for platykurtic distributions, where for small data sets the mid-range is the most efficient estimator.
They are inefficient estimators of location for mesokurtic distributions, such as the normal distribution, and leptokurtic distributions, however.
Read more about this topic: Sample Maximum And Minimum, Applications
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