Pulse Documentation

name: op-synth-poisson
description: Poisson-distributed non-negative integer counts with mean lambda; Knuth multiplicative below 30, normal-approximation above.
kind: operator
category: SYNTH
operator: poisson
type: reference
applies_to: inspect, predict, manifest
examples_tags: [synth, cardinality-analysis]

Synth distributions emit per-row values; no Response.Components.

Use when

Draws whole-number counts of events per period, such as visits per day, around a chosen average.

Questions it answers:

• How many orders might a store get per hour?
• How do I simulate defect counts per batch?

Use something else:

• exponential when you want the time between events, not how many.
• bernoulli when each row is a yes/no outcome.
• discrete when you know the exact share of each count.

Params

• lambda — float, default 1.0. Rate parameter; equals both the mean and the variance. Must be > 0.

Inputs

field type: — numeric: u4/u8/u16/u32/u64, f32/f64. Cast at write time — u4 overflows silently if lambda is large.

Output

Per-row non-negative integer (returned as float64). Two algorithms:

• lambda < 30: Knuth’s multiplicative method — exact, draws k uniforms until product < exp(-lambda).
• lambda >= 30: normal approximation N(lambda, lambda) rounded to nearest non-negative integer.

Gotchas

• Knuth runtime is O(lambda) per row — large lambda would dominate without the normal-approx switch.
• lambda <= 0 → SERVICE_VALIDATION at spec parse.
• Variance equals mean; for over-dispersed counts pair with a lognormal mixer or use rejection sampling via constraints.
• Same (spec, opts.Seed) is deterministic across both algorithm branches.

See

• pulse_examples_search tags=[synth]
• Skills: synthetic-data, op-synth-exponential, op-synth-bernoulli