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PERCENTILE_CONT function

PERCENTILE_CONT is an inverse distribution function that assumes a continuous distribution model. It takes a percentile value and a sort specification, and returns an interpolated value that would fall into the given percentile value with respect to the sort specification.

PERCENTILE_CONT computes a linear interpolation between values after ordering them. Using the percentile value (P) and the number of not null rows (N) in the aggregation group, the function computes the row number after ordering the rows according to the sort specification. This row number (RN) is computed according to the formula RN = (1+ (P*(N-1)). The final result of the aggregate function is computed by linear interpolation between the values from rows at row numbers CRN = CEILING(RN) and FRN = FLOOR(RN).

The final result will be as follows.

If (CRN = FRN = RN) then the result is (value of expression from row at RN)

Otherwise the result is as follows:

(CRN - RN) * (value of expression for row at FRN) + (RN - FRN) * (value of expression for row at CRN).

PERCENTILE_CONT is a compute-node only function. The function returns an error if the query doesn't reference a user-defined table or Amazon Redshift system table.

Syntax

PERCENTILE_CONT(percentile)
WITHIN GROUP(ORDER BY expr)

Arguments

Returns

The return type is determined by the data type of the ORDER BY expression in the WITHIN GROUP clause. The following table shows the return type for each ORDER BY expression data type.

Usage notes

If the ORDER BY expression is a DECIMAL data type defined with the maximum precision of 38 digits, it is possible that PERCENTILE_CONT will return either an inaccurate result or an error. If the return value of the PERCENTILE_CONT function exceeds 38 digits, the result is truncated to fit, which causes a loss of precision.. If, during interpolation, an intermediate result exceeds the maximum precision, a numeric overflow occurs and the function returns an error. To avoid these conditions, we recommend either using a data type with lower precision or casting the ORDER BY expression to a lower precision.

If a statement includes multiple calls to sort-based aggregate functions (LISTAGG, PERCENTILE_CONT, or MEDIAN), they must all use the same ORDER BY values. Note that MEDIAN applies an implicit order by on the expression value.

For example, the following statement returns an error.

SELECT TOP 10 salesid, SUM(pricepaid), 
PERCENTILE_CONT(0.6) WITHIN GROUP(ORDER BY salesid),
MEDIAN(pricepaid)
FROM sales 
GROUP BY salesid, pricepaid;

An error occurred when executing the SQL command:
SELECT TOP 10 salesid, SUM(pricepaid), 
PERCENTILE_CONT(0.6) WITHIN GROUP(ORDER BY salesid),
MEDIAN(pricepaid)
FROM sales 
GROUP BY salesid, pricepaid;

ERROR: within group ORDER BY clauses for aggregate functions must be the same

The following statement runs successfully.

SELECT TOP 10 salesid, SUM(pricepaid), 
PERCENTILE_CONT(0.6) WITHIN GROUP(ORDER BY salesid),
MEDIAN(salesid)
FROM sales 
GROUP BY salesid, pricepaid;

Examples

The following examples use the TICKIT sample database. For more information, see Sample database.

The following example shows that PERCENTILE_CONT(0.5) produces the same results as MEDIAN.

SELECT TOP 10 DISTINCT sellerid, qtysold, 
PERCENTILE_CONT(0.5) WITHIN GROUP(ORDER BY qtysold),
MEDIAN(qtysold) 
FROM sales
GROUP BY sellerid, qtysold;

+----------+---------+-----------------+--------+
| sellerid | qtysold | percentile_cont | median |
+----------+---------+-----------------+--------+
|        2 |       2 |               2 |      2 |
|       26 |       1 |               1 |      1 |
|       33 |       1 |               1 |      1 |
|       38 |       1 |               1 |      1 |
|       43 |       1 |               1 |      1 |
|       48 |       2 |               2 |      2 |
|       48 |       3 |               3 |      3 |
|       77 |       4 |               4 |      4 |
|       85 |       4 |               4 |      4 |
|       95 |       2 |               2 |      2 |
+----------+---------+-----------------+--------+

The following example finds PERCENTILE_CONT(0.5) and PERCENTILE_CONT(0.75) for the quantity sold for each sellerid in the SALES table.

SELECT sellerid, 
PERCENTILE_CONT(0.5) WITHIN GROUP(ORDER BY qtysold) as pct_05,
PERCENTILE_CONT(0.75) WITHIN GROUP(ORDER BY qtysold) as pct_075
FROM sales
GROUP BY sellerid
ORDER BY sellerid
LIMIT 10;

+----------+--------+---------+
| sellerid | pct_05 | pct_075 |
+----------+--------+---------+
|        1 |    1.5 |    1.75 |
|        2 |      2 |    2.25 |
|        3 |      2 |       3 |
|        4 |      2 |       2 |
|        5 |      1 |     1.5 |
|        6 |      1 |       1 |
|        7 |    1.5 |    1.75 |
|        8 |      1 |       1 |
|        9 |      4 |       4 |
|       12 |      2 |    3.25 |
+----------+--------+---------+

To verify the results of the previous query for the first sellerid, use the following example.

SELECT qtysold 
FROM sales 
WHERE sellerid=1;

+---------+
| qtysold |
+---------+
|       2 |
|       1 |
+---------+