---
title: "list_kurtosis_pop"
slug: "dev-database-reference-sql-functions-lists-list-kurtosis-pop"
updated: 2026-10-30T18:19:06Z
published: 2026-10-30T18:19:06Z
canonical: "docs.vastdata.com/dev-database-reference-sql-functions-lists-list-kurtosis-pop"
---

> ## 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_pop

*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 population excess kurtosis of the elements of a numeric list: how heavy the tails are compared with a normal distribution, with no correction for the sample size. It needs at least two non-NULL elements that aren't all the same.

## Syntax

```
list_kurtosis_pop(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_pop`. 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_pop"'

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_pop(l)` treats the non-NULL elements of `l` as a whole population. It divides their fourth central moment by the square of the second and subtracts 3, so that a normal distribution gives about 0:

- `[1.0, 2.0]` gives `-2.0`, the lowest value possible: two equally likely values, no tails.
- `[1.0, 2.0, 3.0, 10.0]` gives `-0.7696000000000001`. The sample form, [list_kurtosis](/develop/docs/dev-database-reference-sql-functions-lists-list-kurtosis), gives `3.227999999999999` for the same list: its correction for the sample size is large for short lists.
- The calculation is in floating point, so a result can be a little off its exact value: `[1.0, 2.0, 3.0]` gives `-1.4999999999999787`, not `-1.5`.
- A single element, or elements that are all the same, give NULL.

## NULLs and edge cases

| Input | Result |
| --- | --- |
| `NULL`, or `NULL::BIGINT[]` | `NULL` |
| `[]::DOUBLE[]` (empty list) | `NULL` |
| `[NULL, NULL]::DOUBLE[]` | `NULL` |
| `[1.0]` | `NULL` |
| `[5, 5, 5, 5]` | `NULL` |
| `[1.0, 2.0]` | `-2.0` |
| `[1.0, 2.0, 3.0]` | `-1.4999999999999787` |
| `typeof(list_kurtosis_pop([1, 2]))` | `&apos;DOUBLE&apos;` |
| A list holding `NaN` or infinity, or values that overflow (`[1e308, -1e308, 1e308]`) | Error: `Kurtosis is out of range!` |
| 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-pop#set-up-the-examples):

```
run("SELECT list_kurtosis_pop(NULL), list_kurtosis_pop(NULL::BIGINT[]), list_kurtosis_pop([]::DOUBLE[]), "
    "list_kurtosis_pop([NULL, NULL]::DOUBLE[])")
run("SELECT list_kurtosis_pop([1.0]), list_kurtosis_pop([5, 5, 5, 5]), list_kurtosis_pop([1.0, 2.0]), "
    "list_kurtosis_pop([1.0, 2.0, 3.0]), typeof(list_kurtosis_pop([1, 2]))")
run("SELECT list_kurtosis_pop(['NaN'::DOUBLE, 1.0, 2.0])")
run("SELECT list_kurtosis_pop(['inf'::DOUBLE, 1.0, 2.0])")
run("SELECT list_kurtosis_pop([1e308, -1e308, 1e308])")
run(f"SELECT list_kurtosis_pop(123) FROM {TABLE} LIMIT 1")
```

```
[(None, None, None, None)]
[(None, None, -2.0, -1.4999999999999787, 'DOUBLE')]
OSError: Kurtosis is out of range!
OSError: Kurtosis is out of range!
OSError: Kurtosis 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 kurtosis of each row's numbers. Row 2's `[3, NULL, 3]` has no spread, so its result is NULL, as are the empty list and the NULL list:

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

```
[(1, [1, 2, 3], -1.4999999999999787), (2, [3, None, 3], None), (3, [], None), (4, None, None), (5, [-5, 0, -5, 10], -1.0)]
```

The rows whose numbers are spread more evenly than a normal distribution:

```
run(f"SELECT id, nums FROM {TABLE} WHERE list_kurtosis_pop(nums) < 0 ORDER BY id LIMIT 10")
```

```
[(1, [1, 2, 3]), (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_pop()` always runs in the Query Engine:

- **In the `SELECT` list,** a projection step computes `list_kurtosis_pop()` for each row the scan returns.
- **In `WHERE`,** the scan sends the list for every row, and a `FILTER` step computes `list_kurtosis_pop()` 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_pop(nums) < 0")
```

```
┌───────────────────────────┐
│         PROJECTION        │
│    ────────────────────   │
│             #1            │
│                           │
└─────────────┬─────────────┘
┌─────────────┴─────────────┐
│           FILTER          │
│    ────────────────────   │
│  (list_aggr(CAST(nums AS  │
│  DOUBLE[]), 'kurtosis_pop'│
│          ) < 0.0)         │
│                           │
└─────────────┬─────────────┘
┌─────────────┴─────────────┐
│         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 &gt; 1`, is evaluated in VAST DataBase, so `list_kurtosis_pop()` 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 &lt; 0` is pushed down, `list_kurtosis_pop(nums) &lt; 0` 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 `Kurtosis 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_kurtosis_pop`:

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

```
OSError: Kurtosis is out of range!
```

- **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_pop` 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_pop` | population excess kurtosis | 2 | `-0.7696000000000001` |
| [list_kurtosis](/develop/docs/dev-database-reference-sql-functions-lists-list-kurtosis) | sample excess kurtosis, corrected for the sample size | 4 | `3.227999999999999` |
| [list_skewness](/develop/docs/dev-database-reference-sql-functions-lists-list-skewness) | sample skewness: asymmetry | 3 | `1.763632614803888` |

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

```
[(-0.7696000000000001, 3.227999999999999, 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_kurtosis](/develop/docs/dev-database-reference-sql-functions-lists-list-kurtosis): the sample form.
- [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.