window_stdev

Knowledge Checkpoint

Readings that will help you understand this documentation better:

• Window Functions Overview

Definition

A window aggregation function that returns the (sample) standard deviation of rows in a range relative to the current row.

Syntax

window_stdev(agg_expr)
window_stdev(agg_expr, order: order_expr, ...)
window_stdev(agg_expr, range, order: order_expr, ...)
window_stdev(agg_expr, range, order: order_expr, ..., reset: partition_expr, ...)
window_stdev(agg_expr, range, order: order_expr, ..., partition: partition_expr, ...)

Examples

window_stdev(count(users.id))
window_stdev(count(users.id), order: count(users.id) | desc())
window_stdev(count(users.id), -2..2, order: users.created_at | month())
window_stdev(count(users.id), order: users.created_at | month(), reset: users.gender)

Input

• agg_expr (required): An aggregation expression that we want to find the (sample) standard deviation of.
• range (optional): A range of rows to include in the (sample) standard deviation. Negative values indicate rows before the current row, and positive values indicate rows after the current row, while 0 indicates the current row. If the beginning or end of the range is not specified, the range will include all rows from the beginning or end of the table. By default, if the range is not specified:
  • If order is specified, the range is ..0 (from the first row to the current row).
  • If order is not specified, the range is .. (from the first row to the last row).
• order (required, repeatable): A field that is used for ordering. The order is default to ascending. The order can be set explicitly with asc() or desc().
  danger

  If the specified order does not uniquely identify rows, the result of the function can be non-deterministic. For example, if you use order: users.age, and there are multiple users with the same age in the same partition, the result can be unexpected.

• partition or reset (repeatable, optional): A field that is used for partitioning the table. If partitions are not specified:
  • If order is specified, the table will be partitioned by all other grouping columns.
  • If order is not specified, the table will be considered as a single partition.

Output

The (sample) standard deviation of the current row and the rows within the specified range.

Sample Usages

The most common use case for window_stdev is to draw a Process Behavior Chart (PBC) for a process. The PBC is a type of control chart that shows the process variation over time. The window_stdev function can be used to calculate the standard deviation of a process variable over a range of time periods. This can help you identify when the process is out of control and needs to be adjusted.

Here is an example of how you can use window_stdev to create an PBC in Holistics:

Process Behavior Chart AQL

explore {
  dimensions {
    orders.created_at | month()
  }
  measures {
    count(orders.id),
    upper: window_avg(count(orders.id), ..) + window_stdev(count(orders.id), ..),
    mean: window_avg(count(orders.id), ..),
    lower: window_avg(count(orders.id), ..) - window_stdev(count(orders.id), ..),
  }
}

Open in AMQL playground

Result

SQL

WITH "aql__t1" AS (
  SELECT
    (DATE_TRUNC ( 'month', (CAST ( "orders"."created_at" AS timestamptz )) AT TIME ZONE 'Asia/Saigon' )) AT TIME ZONE 'Asia/Saigon' AS "orders->created_at->month",
    COUNT("orders"."id") AS "count_orders->id"
  FROM
    "demo"."orders" "orders"
  GROUP BY
    1
)
SELECT
  TO_CHAR((CAST ( "aql__t1"."orders->created_at->month" AS timestamptz )) AT TIME ZONE 'Asia/Saigon', 'YYYY-MM-DD HH24:MI:SS.US') AS "orders->created_at->month",
  "aql__t1"."count_orders->id" AS "count_orders->id",
  ((AVG("aql__t1"."count_orders->id") OVER (  ROWS BETWEEN UNBOUNDED PRECEDING AND UNBOUNDED FOLLOWING)) + (STDDEV_SAMP ( "aql__t1"."count_orders->id" ) OVER (  ROWS BETWEEN UNBOUNDED PRECEDING AND UNBOUNDED FOLLOWING))) AS "upper",
  AVG("aql__t1"."count_orders->id") OVER (  ROWS BETWEEN UNBOUNDED PRECEDING AND UNBOUNDED FOLLOWING) AS "mean",
  ((AVG("aql__t1"."count_orders->id") OVER (  ROWS BETWEEN UNBOUNDED PRECEDING AND UNBOUNDED FOLLOWING)) - (STDDEV_SAMP ( "aql__t1"."count_orders->id" ) OVER (  ROWS BETWEEN UNBOUNDED PRECEDING AND UNBOUNDED FOLLOWING))) AS "lower"
FROM
  "aql__t1"
WHERE
  "aql__t1"."count_orders->id" IS NOT NULL