# Poisson Distribution Calculator

> Poisson Distribution Calculator is a paid API for AI agents from kihustle.tech, paid per call via x402, $0.002/call, status unknown (last checked 2026-09-13).

Computes the Poisson probability mass function P(X=k) given an event rate (lambda) and a count (k)

## Facts

- Endpoint: POST https://kihustle.tech/api/v1/poisson-distribution
- Price: $0.002/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-13
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/poisson-distribution-calculator-fc55c9bb
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_OZkmZDJ0mj77fIi_3jmcA

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability poisson-distribution-calculator-fc55c9bb -d '<json body>'
```

Example prompt: What is the Poisson probability of exactly 3 events occurring if the average rate is 2.5 events per interval?

## When to prefer this

Use this endpoint when you need a quick, pay-per-call Poisson PMF computation without setting up a local math library or stats environment. Best suited for agents performing probabilistic modeling of rare or discrete events (arrivals, defects, failures) where k and lambda are already known.

## Known failure modes

- Missing or non-integer k value returns an error
- Negative lambda_rate may cause computation failure
- Malformed JSON body results in a 400-level error
- Very large k values may cause numerical overflow
- Payment not included or invalid returns a 402 response

## How this service works

Kostenlose Guides, Solo-Playbooks und Artikel zu KI, Automation und Side Hustles — für Menschen, die mit echten Systemen online Einkommen aufbauen wollen. Transparent finanziert über faire Affiliate-Links.

## Output

Returns a JSON object with a computed Poisson probability result and a success status indicator, representing P(X=k) for the given lambda_rate and k values.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "k": {
   "type": "integer"
  },
  "lambda_rate": {
   "type": "number"
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "type": "json",
 "example": {
  "result": "processed",
  "status": "success"
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/poisson-distribution-calculator-fc55c9bb/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from kihustle.tech](https://www.zero.xyz/host/kihustle.tech/llms.txt)