For each observation corresponding to a row in the group of series, compute the q-quantile of the values for the observation using the Rankit-Cleveland quantile definition, for .
To compute the -quantile, first find , the smallest rank such that,
where the order statistics represent data for the series ordered from low to high, and is the Rankit-Cleveland definition of the empirical distribution function: . For purposes of computing , tied ranks are assumed to take the last tied value.
Then the quantile is computed as
where the interpolating constant is
for the smallest integer where . In the leading case where there are no tied values, .
Examples
show @rquantile(g, 0.25
returns a linked series of the 25th percentiles in the rows of group g.