---
title: "list_kurtosis"
slug: "dev-database-reference-sql-functions-lists-list-kurtosis"
updated: 2026-10-30T18:19:11Z
published: 2026-10-30T18:19:11Z
canonical: "docs.vastdata.com/dev-database-reference-sql-functions-lists-list-kurtosis"
---

> ## 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_kurtosis

*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 excess kurtosis of the elements of a numeric list: how heavy the tails are compared with a normal distribution. It needs at least four non-NULL elements.

## Syntax

```
list_kurtosis(l)
```

| Argument | Type | Description |
| --- | --- | --- |
| `l` | a list of numbers | The values whose kurtosis 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_kurtosis`. 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_kurtosis"'

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, "<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_kurtosis(l)` measures the tails of the `n` non-NULL elements of `l`. It's the sample excess kurtosis: the fourth central moment divided by the square of the second, minus 3, then corrected for the sample size as `((n+1) &#xd7; that + 6) &#xd7; (n-1) / ((n-2)(n-3))`.

- A normal distribution has an excess kurtosis of about 0. A positive result means more of the spread comes from a few far values; a negative one, that the values are spread more evenly.
- `[1.0, 2.0, 3.0, 10.0]` gives `3.227999999999999`: the `10.0` stands far from the others. `[1.0, 2.0, 3.0, 10.0, 11.0]` gives `-3.0410826680608927`: two groups, no single far value.
- Fewer than four non-NULL elements give NULL.
- Elements that are all the same give NULL.

For the population form, which needs fewer elements and has no correction, use [list_kurtosis_pop](/develop/docs/dev-database-reference-sql-functions-lists-list-kurtosis-pop).

## 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]`, `[1.0, 2.0, 3.0]` | `NULL` (fewer than four elements) |
| `[5, 5, 5, 5]` | `NULL` |
| `[1.0, 2.0, 3.0, 10.0, 11.0]` | `-3.0410826680608927` |
| `typeof(list_kurtosis([1, 2]))` | `&apos;DOUBLE&apos;` |
| A number, string, `BLOB`, date or boolean | Error: `No function matches the given name and argument types`, for example `&apos;list_aggr(INTEGER_LITERAL, STRING_LITERAL)&apos;` |

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-kurtosis#set-up-the-examples):

```
run("SELECT list_kurtosis(NULL), list_kurtosis(NULL::BIGINT[]), list_kurtosis([]::DOUBLE[]), "
    "list_kurtosis([NULL, NULL]::DOUBLE[])")
run("SELECT list_kurtosis([1.0]), list_kurtosis([1.0, 2.0]), list_kurtosis([1.0, 2.0, 3.0]), list_kurtosis([5, 5, 5, 5])")
run("SELECT list_kurtosis([1.0, 2.0, 3.0, 10.0, 11.0]), typeof(list_kurtosis([1, 2]))")
run(f"SELECT list_kurtosis(123) FROM {TABLE} LIMIT 1")
```

```
[(None, None, None, None)]
[(None, None, None, None)]
[(-3.0410826680608927, 'DOUBLE')]
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 kurtosis of each row's numbers and measurements. Only row 5's numbers `[-5, 0, -5, 10]` have four elements; they give `1.5`. Every other result is NULL, including all the measurements, which have at most three elements:

```
run(f"SELECT id, nums, list_kurtosis(nums), list_kurtosis(vals) FROM {TABLE} ORDER BY id LIMIT 10")
```

```
[(1, [1, 2, 3], None, None), (2, [3, None, 3], None, None), (3, [], None, None), (4, None, None, None), (5, [-5, 0, -5, 10], 1.5, None)]
```

The rows with a kurtosis to report:

```
run(f"SELECT id, nums FROM {TABLE} WHERE list_kurtosis(nums) IS NOT NULL 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_kurtosis()` always runs in the Query Engine:

- **In the `SELECT` list,** a projection step computes `list_kurtosis()` for each row the scan returns.
- **In `WHERE`,** the scan sends the list for every row, and a `FILTER` step computes `list_kurtosis()` 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_kurtosis(nums) IS NOT NULL")
```

```
┌───────────────────────────┐
│         PROJECTION        │
│    ────────────────────   │
│             #1            │
│                           │
└─────────────┬─────────────┘
┌─────────────┴─────────────┐
│           FILTER          │
│    ────────────────────   │
│  (list_aggr(CAST(nums AS  │
│  DOUBLE[]), 'kurtosis') IS│
│          NOT NULL)        │
│                           │
└─────────────┬─────────────┘
┌─────────────┴─────────────┐
│         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 &gt; 1`, is evaluated in VAST DataBase, so `list_kurtosis()` runs only on the rows that pass it. The plan for `id &gt; 1` alone has no `FILTER` step:

```
plan(f"SELECT id FROM {TABLE} WHERE id > 1")
```

```
┌───────────────────────────┐
│         VAST_SCAN         │
│    ────────────────────   │
│    Function: VAST_SCAN    │
│      Projections: id      │
│                           │
└───────────────────────────┘
```

- **Store the kurtosis if you filter on it often.** Compute it when you write the rows and keep it in its own column: `kurtosis &gt; 1` is pushed down, `list_kurtosis(nums) &gt; 1` isn't.

## Limitations and errors

- **Short lists give NULL.** With fewer than four non-NULL elements, the result is NULL rather than an error. Use [list_kurtosis_pop](/develop/docs/dev-database-reference-sql-functions-lists-list-kurtosis-pop) for shorter lists.
- **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_kurtosis` runs on, and its accepted form `list_aggr(ANY[], VARCHAR, [ANY...]) -&gt; ANY`.
- **`ORDER BY` needs a `LIMIT`.** Without one, the query fails with `The operator &apos;ORDER_BY&apos; 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_kurtosis` | sample excess kurtosis | 4 | `3.227999999999999` |
| [list_kurtosis_pop](/develop/docs/dev-database-reference-sql-functions-lists-list-kurtosis-pop) | population excess kurtosis, no sample-size correction | 2 | `-0.7696000000000001` |
| [list_skewness](/develop/docs/dev-database-reference-sql-functions-lists-list-skewness) | sample skewness: asymmetry | 3 | `1.763632614803888` |

```
run("SELECT list_kurtosis(l), list_kurtosis_pop(l), list_skewness(l) FROM (SELECT [1.0, 2.0, 3.0, 10.0]::DOUBLE[] AS l)")
```

```
[(3.227999999999999, -0.7696000000000001, 1.763632614803888)]
```

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_skewness](/develop/docs/dev-database-reference-sql-functions-lists-list-skewness): how lopsided a list's values 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.