Pulse Documentation

name: op-agg-kurtosis
description: Population excess kurtosis g2 (m4 / m2^2 - 3, dividing by n) via online moments.
kind: operator
category: AGG
operator: AGG_KURTOSIS
type: reference
applies_to: process, compose, predict
examples_tags: [distribution-shape, streaming-friendly]

Use when

How heavy a numeric field’s tails are next to a normal distribution: positive when extreme values are more common.

Questions it answers:

• Do transaction amounts have more extreme values than a bell curve would give?
• Are response times prone to rare, very long waits?

Use something else:

• AGG_SKEWNESS when you want to know whether the field is lopsided.

Params

Weight-aware ("weight": null opts out): weighted population moments, Σw in place of n. Invalid weights excluded (PULSE_WEIGHT_INVALID_ROWS).

Inputs

Output

Scalar float64 — population excess kurtosis g2 = m4 / m2^2 − 3 (moments divide by n), NOT the adjusted G2 of Excel KURT / SPSS. Per-group when wired under a grouper.

Reading the output

• value: How heavy the tails are next to a normal distribution. Pulse computes the population EXCESS kurtosis g2: the average fourth-power z-score minus 3, (m4/n) / (m2/n)^2 - 3, where the components m2 and m4 are SUMS of squared and fourth-power distances from the mean (not yet divided by n), so a normal distribution scores 0. It can never fall below -2.
  • Caveat: Small-n bias: g2 differs from the adjusted G2 that Excel KURT and SPSS print, and on small groups the gap is large; neither is stable on a handful of rows.

Components

Weighted adds floor sum_weights, n_eff (probability), n_weight_invalid.

Universal floor {n, n_null} plus operator-specific:

• Mergeability: Mergeable (Chan moments combine)
• Streaming: per-chunk online moments

Gotchas

• n <= 1 or zero variance → 0 (not NaN): check n before reading a 0.
• Small-n bias vs adjusted G2 is large on small groups; g2 ≥ −2 always.
• Excess kurtosis (normal = 0), NOT raw kurtosis (normal = 3).
• decimal128 rejected.

See

• pulse_examples_search tags=[distribution-shape]
• Skills: aggregation-design, response-components