The percentile_cont and percentile_disc window functions are available in columnstore and many other databases. These allow calculation of percentiles. Percentile_cont will average 2 rows if one is not identified while Percentile_disc picks the first row in the window. Finally a median function should exist which is equivalent to percentile_cont(0.5).

These have slightly different syntax than other window function to specify the column:

percentile_cont(0.5) within group (order by amount) over (partition by owner) pct_cont,
percentile_disc(0.5) within group (order by amount) over (partition by owner) pct_disc

Some investigation

percentile_cont and percentile_disc are not specifically window functions. They originally are "ordered-set aggregate functions" (#1) which one can also use as window functions (#2):

Ordered-set aggreates

The syntax for case #1:

  percentile_cont(fraction) WITHIN GROUP (ORDER BY sort_expression)

Note the lack of OVER clause.
Ordered-set aggregate functions are supported by:

• https://www.postgresql.org/docs/current/static/functions-aggregate.html
• http://docs.aws.amazon.com/redshift/latest/dg/c_Aggregate_Functions.html
  Neither MariaDB nor MySQL support any "ordered-set aggregate functions".

Ordered-set aggregates as window functions

Syntax for case #2 (ordered-set aggregate, used as window function)

• http://docs.aws.amazon.com/redshift/latest/dg/r_WF_PERCENTILE_DISC.html
• https://docs.oracle.com/cd/B12037_01/server.101/b10759/functions100.htm#i1000909

PERCENTILE_DISC ( percentile )

WITHIN GROUP (ORDER BY expr)

OVER (  [ PARTITION BY expr_list ]  )

(BTW: note that PostgreSQL doesn't support ordered-set-aggregates-as-window functions: https://www.postgresql.org/docs/current/static/functions-window.html ,

any built-in or user-defined normal aggregate function (but not ordered-set or hypothetical-set aggregates) can be used as a window function)