--- title: "list_skewness" slug: "dev-database-reference-sql-functions-lists-list-skewness" updated: 2026-10-30T18:19:06Z published: 2026-10-30T18:19:06Z canonical: "docs.vastdata.com/dev-database-reference-sql-functions-lists-list-skewness" --- > ## Documentation Index > Fetch the complete documentation index at: https://docs.vastdata.com/llms.txt > Use this file to discover all available pages before exploring further. # list_skewness *Applies to VAST Cluster 5.5.* *[Functions](/develop/docs/dev-database-reference-sql-functions-index) › [List, struct and map functions](/develop/docs/dev-database-reference-sql-functions-lists-and-structs) › Aggregate a list.* Returns the sample skewness of the elements of a numeric list: how lopsided the values are around their mean. It needs at least three non-NULL elements. ## Syntax ``` list_skewness(l) ``` | Argument | Type | Description | | --- | --- | --- | | `l` | a list of numbers | The values whose skewness is computed. | **Returns:** `DOUBLE`. ## Set up the examples The examples connect with the ADBC driver, as in [VAST Query Engine (ADBC)](/develop/docs/dev-database-integrations-adbc), and work in a schema called `docs_sql_fn_lists_list_skewness`. Set `QE_ENDPOINT`, `AWS_ACCESS_KEY_ID`, `AWS_SECRET_ACCESS_KEY` and `VASTDB_BUCKET` ([SQL reference](/develop/docs/dev-database-reference-sql-index#example-connect-and-use-a-transaction)), and run the blocks in order in one Python session. Below each block is the output you should see. This block connects, defines the `run()` and `plan()` helpers, and creates a table of five rows of lists: whole numbers (`nums`) and measurements (`vals`). Row 2 has a NULL element, row 3 has empty lists, row 4 has no values, and row 5's measurements are close to the largest `DOUBLE`: ``` import os import re import adbc_driver_manager import adbc_driver_manager.dbapi as dbapi import adbc_driver_vastdb BUCKET = os.environ["VASTDB_BUCKET"] SCHEMA = f'"{BUCKET}/docs_sql_fn_lists_list_skewness"' conn = dbapi.connect( driver=adbc_driver_vastdb.get_driver_path(), db_kwargs={ "vast.db.endpoint": os.environ["QE_ENDPOINT"], "vast.db.access_key": os.environ["AWS_ACCESS_KEY_ID"], "vast.db.secret_key": os.environ["AWS_SECRET_ACCESS_KEY"], }, autocommit=True, ) def server_message(e): """The server's message in a driver error, without the request ID or the echoed statement.""" text = re.sub(r"\[req=0x[0-9a-f]+\]: ", "", str(e)) found = (re.search(r'message: "(.*?)", request_id', text, re.S) or re.search(r"description: (.*)\)", text, re.S)) message = found.group(1) if found else text.strip().splitlines()[-1] message = re.sub(r"^Plan query: '.*?' failed with: ", "", message, flags=re.S) message = re.split(r"\\n|\n", message)[0].replace('\\"', '"') return message.replace(BUCKET, "") def run(sql): """Run one statement. Print the rows it returns, or the error.""" try: with conn.cursor() as cur: cur.execute(sql) rows = cur.fetchall() if cur.description else [] except (adbc_driver_manager.Error, OSError) as e: print(f"{type(e).__name__}: {server_message(e)}") else: print(rows) def plan(sql): """Print the plan without its ~N Rows lines: the table's row count, which can still be 0 just after an insert.""" with conn.cursor() as cur: cur.execute("EXPLAIN " + sql) steps = cur.fetchall()[0][1] print("\n".join(line for line in steps.splitlines() if "Rows" not in line)) TABLE = f"{SCHEMA}.samples" run(f"CREATE SCHEMA IF NOT EXISTS {SCHEMA}") run(f"CREATE TABLE IF NOT EXISTS {TABLE} (id BIGINT, nums BIGINT[], vals DOUBLE[])") run(f"INSERT INTO {TABLE} VALUES " "(1, [1, 2, 3], [0.5, 2.5, -1.0]), " "(2, [3, NULL, 3], [2.0, NULL]), " "(3, [], []), " "(4, NULL, NULL), " "(5, [-5, 0, -5, 10], [1e308, 1e308, -1e-308])") ``` ``` [] [] [(5,)] ``` ## What it does `list_skewness(l)` measures the asymmetry of the `n` non-NULL elements of `l`. It's the sample skewness: the third central moment divided by the second raised to the power 1.5, multiplied by `sqrt(n(n-1)) / (n-2)` to correct for the sample size. - A symmetric list gives `0.0`: `[1.0, 2.0, 3.0]`. - A long tail of high values gives a positive result: `[1.0, 2.0, 10.0]` gives `1.6523167403329886` and `[1.0, 2.0, 3.0, 10.0]` gives `1.763632614803888`. - Fewer than three non-NULL elements give NULL. - Elements that are all the same give `NaN`, not NULL: there's no spread to divide by. ## NULLs and edge cases | Input | Result | | --- | --- | | `NULL`, or `NULL::BIGINT[]` | `NULL` | | `[]::DOUBLE[]` (empty list) | `NULL` | | `[NULL, NULL]::DOUBLE[]` | `NULL` | | `[1.0]`, `[1.0, 2.0]` | `NULL` (fewer than three elements) | | `[1.0, 2.0, 3.0]` | `0.0` | | `[5, 5, 5, 5]` | `NaN` (Python shows `nan`) | | `typeof(list_skewness([1, 2]))` | `'DOUBLE'` | | A list holding `NaN` or infinity, or values that overflow (`[1e308, -1e308, 1e308]`) | Error: `SKEW is out of range!` | | A number, string, `BLOB`, date or boolean | Error: `No function matches the given name and argument types`, for example `'list_aggr(INTEGER_LITERAL, STRING_LITERAL)'` | The same cases, as the cluster returns them. They use the table and helpers from [Set up the examples](/develop/docs/dev-database-reference-sql-functions-lists-list-skewness#set-up-the-examples): ``` run("SELECT list_skewness(NULL), list_skewness(NULL::BIGINT[]), list_skewness([]::DOUBLE[]), " "list_skewness([NULL, NULL]::DOUBLE[])") run("SELECT list_skewness([1.0]), list_skewness([1.0, 2.0]), list_skewness([1.0, 2.0, 3.0]), list_skewness([5, 5, 5, 5]), " "typeof(list_skewness([1, 2]))") run("SELECT list_skewness(['NaN'::DOUBLE, 1.0, 2.0])") run("SELECT list_skewness(['inf'::DOUBLE, 1.0, 2.0])") run("SELECT list_skewness([1e308, -1e308, 1e308])") run(f"SELECT list_skewness(123) FROM {TABLE} LIMIT 1") ``` ``` [(None, None, None, None)] [(None, None, 0.0, nan, 'DOUBLE')] OSError: SKEW is out of range! OSError: SKEW is out of range! OSError: SKEW is out of range! InternalError: Binder Error: No function matches the given name and argument types 'list_aggr(INTEGER_LITERAL, STRING_LITERAL)'. You might need to add explicit type casts. ``` ## Examples The skewness of each row's numbers. Row 1 is symmetric (`0.0`), and row 5's `10` gives it a positive skew. Row 2 has only two non-NULL elements, so its result is NULL: ``` run(f"SELECT id, nums, list_skewness(nums) FROM {TABLE} ORDER BY id LIMIT 10") ``` ``` [(1, [1, 2, 3], 0.0), (2, [3, None, 3], None), (3, [], None), (4, None, None), (5, [-5, 0, -5, 10], 1.4142135623730951)] ``` The rows whose numbers lean towards high values: ``` run(f"SELECT id, nums FROM {TABLE} WHERE list_skewness(nums) > 1 ORDER BY id LIMIT 10") ``` ``` [(5, [-5, 0, -5, 10])] ``` ## How it runs in VAST The Query Engine runs on the cluster's CNodes, and a query on a table starts with a scan in VAST DataBase (`VAST_SCAN`). The scan reads a list column whole, and `list_skewness()` always runs in the Query Engine: - **In the `SELECT` list,** a projection step computes `list_skewness()` for each row the scan returns. - **In `WHERE`,** the scan sends the list for every row, and a `FILTER` step computes `list_skewness()` and keeps the rows that match. No rows are skipped in storage. The plan of the `WHERE` example shows the `FILTER` step above the scan: ``` plan(f"SELECT id FROM {TABLE} WHERE list_skewness(nums) > 1") ``` ``` ┌───────────────────────────┐ │ PROJECTION │ │ ──────────────────── │ │ #1 │ │ │ └─────────────┬─────────────┘ ┌─────────────┴─────────────┐ │ FILTER │ │ ──────────────────── │ │ (list_aggr(CAST(nums AS │ │ DOUBLE[]), 'skewness') > │ │ 1.0) │ │ │ └─────────────┬─────────────┘ ┌─────────────┴─────────────┐ │ VAST_SCAN │ │ ──────────────────── │ │ Function: VAST_SCAN │ │ │ │ Projections: │ │ nums │ │ id │ │ │ └───────────────────────────┘ ``` ## Make it faster - **Add a condition on a plain column.** A comparison of a column with a constant, such as `id > 1`, is evaluated in VAST DataBase, so `list_skewness()` runs only on the rows that pass it. The plan for `id > 1` alone has no `FILTER` step: ``` plan(f"SELECT id FROM {TABLE} WHERE id > 1") ``` ``` ┌───────────────────────────┐ │ VAST_SCAN │ │ ──────────────────── │ │ Function: VAST_SCAN │ │ Projections: id │ │ │ └───────────────────────────┘ ``` - **Store the skewness if you filter on it often.** Compute it when you write the rows and keep it in its own column: `skew > 1` is pushed down, `list_skewness(nums) > 1` isn't. ## Limitations and errors - **`NaN`, infinity and overflow fail the whole query.** If any row's list holds `NaN` or an infinite value, or values large enough to overflow a `DOUBLE` in the calculation, the query fails with `SKEW is out of range!` and returns no rows. Row 5's measurements (`1e308` twice) are enough. Keep such values out of the lists you pass to `list_skewness`: ``` run(f"SELECT id, list_skewness(vals) FROM {TABLE} ORDER BY id LIMIT 10") ``` ``` OSError: SKEW is out of range! ``` - **A list of equal values gives `NaN`, not NULL.** See [NULLs and edge cases](/develop/docs/dev-database-reference-sql-functions-lists-list-skewness#nulls-and-edge-cases). - **Lists only.** Any other type fails with `No function matches the given name and argument types`. The error names `list_aggr`, the list aggregate that `list_skewness` runs on, and its accepted form `list_aggr(ANY[], VARCHAR, [ANY...]) -> ANY`. - **`ORDER BY` needs a `LIMIT`.** Without one, the query fails with `The operator 'ORDER_BY' type=1 is currently not supported for this usage`. ## Similar functions | Function | What it computes | Fewest elements | Result for `[1.0, 2.0, 3.0, 10.0]::DOUBLE[]` | | --- | --- | --- | --- | | `list_skewness` | sample skewness: asymmetry | 3 | `1.763632614803888` | | [list_kurtosis](/develop/docs/dev-database-reference-sql-functions-lists-list-kurtosis) | sample excess kurtosis: weight of the tails | 4 | `3.227999999999999` | | [list_kurtosis_pop](/develop/docs/dev-database-reference-sql-functions-lists-list-kurtosis-pop) | population excess kurtosis | 2 | `-0.7696000000000001` | ``` run("SELECT list_skewness(l), list_kurtosis(l), list_kurtosis_pop(l) FROM (SELECT [1.0, 2.0, 3.0, 10.0]::DOUBLE[] AS l)") ``` ``` [(1.763632614803888, 3.227999999999999, -0.7696000000000001)] ``` Clean up: ``` run(f"DROP TABLE IF EXISTS {TABLE}") run(f"DROP SCHEMA IF EXISTS {SCHEMA}") conn.close() ``` ``` [] [] ``` ## See also - [List, struct and map functions](/develop/docs/dev-database-reference-sql-functions-lists-and-structs): all the list functions. - [list_kurtosis](/develop/docs/dev-database-reference-sql-functions-lists-list-kurtosis): how heavy a list's tails are. - [Where filters run](/develop/docs/dev-database-reference-sql-select#where-filters-run) and [pushdowns](/develop/docs/dev-database-reference-pushdowns). - [EXPLAIN](/develop/docs/dev-database-reference-sql-explain): how to read a plan.