How to define the median for bivariate function?

Question

I know if we define a function f(x) and its cdf is F(x). The inverse function of cdf is inverseF.

I can define its median as follows: median = inverseF(0.5).

But if I want to get the median for a bivariate function f(x,y). How to define it? Thanks very much!

You mean a distribution function $f(x)$ - right? Similar to Bob Jansen answer, the search for the notion of a quantile in higher dimensions is much more complicated than in dimension 1. — Richard, May 27 '14 at 9:47

Community · Accepted Answer · 2017-04-13 12:44:17Z

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The standard median is not defined in multiple dimensions but a generalized notion exists as explained in this CrossValidated answer.

Community♦

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answered May 24 '14 at 16:18

Bob Jansen♦

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