@cumbquantile |

Cumulative quantiles of a series.

Increasing samples calculation of the quantile value where approximately 100*q percent of the data is less than or equal to the value,

Syntax: @cumbquantile(x, q, [s])

x: series

q: number, series

s: (optional) sample string or object

Return: series

• The quantile value q must satisfy .

• The cumulative quantiles are computed using the Rankit-Cleveland definition of the empirical distribution function: .

To compute the cumulative backward quantile for observation find , the smallest rank such that:

where the order statistics represent data for the observations (), ordered from low to high, and is the last period. 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, .

This function is panel aware.

Examples

show @cumbquantile(x, 0.1)

generates a linked series of the backward cumulative 10th percentile of the series x.

Cross-references

See also
@cumbmedian.

For the forward variant of this function, see
@cumquantile.