Why does one interested in modelling the distribution of median of random samples?

Asked Apr 27 '23 at 18:20

Active Apr 28 '23 at 21:24

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I was reading this article which introduce the families of distribution for the median of an random sample. However, the writer did not state the reason why one is interested in modelling the distribution of the median of a random sample.

I found articles that related to this in here and here but they still did not mention why. I do know that median, unlike mean, is insensitive to outliers and in the case of Laplace distribution the median is the MLE, but I'm not sure it is related to my question? Any insight why?

edited Apr 28 '23 at 05:32

asked Apr 27 '23 at 18:20

fletcherwrw

2

Medians are useful because they tell us where the "middle" of a distribution is without being influenced by extreme values. Studying how any statistic behaves when applied to known distributions is a great way to build intuition about the behavior of that statistic. – John Madden Apr 27 '23 at 18:41
Imo, medians are a lot more interpretable than the mean. – Alex J Apr 27 '23 at 23:01
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The population median always exists for a random variable, whereas the population mean does not. – Galen Apr 28 '23 at 04:00
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If you are a working forecaster, and your bonus depends on minimizing the Mean Absolute Error (MAE) of your forecasts, you should be very interested in the conditional median, indeed, because using the median of your predictive distribution as a point forecast will minimize the expected MAE. – Stephan Kolassa Apr 28 '23 at 08:28

Why does one interested in modelling the distribution of median of random samples?

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