KURTOSIS

Applies to: ✅ Data 360 SQL ✅ Tableau Hyper API

Computes the unbiased excess kurtosis of input values. Excess kurtosis measures how heavy-tailed a distribution is relative to a normal distribution: positive values indicate heavier tails and more frequent outliers, negative values indicate lighter tails, and zero matches the normal distribution.

Syntax

kurtosis(<expression>)

Arguments

Required

<expression>: An expression of any numerical type.

Returns

Returns a double precision value.

Returns NULL when fewer than four non-null input values are provided or when all non-null values are identical.

Considerations

Returns excess kurtosis (Fisher definition): a normal distribution has KURTOSIS of 0, not 3. Add 3 to convert to raw (Pearson) kurtosis.
Uses an unbiased sample formula with finite-sample bias correction.
Ignores NULL inputs. Any NaN or infinite input propagates to a NaN result.

Examples

Calculate Excess Kurtosis

Find the excess kurtosis of response times.

SELECT kurtosis(latency_ms) AS latency_kurtosis
FROM request_logs;

Kurtosis by Group

Compute kurtosis for each endpoint to flag those whose latency has the heaviest tails.

SELECT endpoint, kurtosis(latency_ms) AS latency_kurtosis
FROM request_logs
GROUP BY endpoint
ORDER BY latency_kurtosis DESC;

Summarize Distribution Shape

Report skewness and kurtosis side by side to summarize the shape of daily returns per ticker.

SELECT
    ticker,
    skewness_samp(return_pct) AS return_skew,
    kurtosis(return_pct)      AS return_kurtosis
FROM daily_returns
GROUP BY ticker;