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Poisson Distribution Calculator
x402
Poisson Distribution Calculator is a paid API for AI agents from distribution.openverbs.com, paid per call via x402, $0.004/call, status unknown (last checked 2026-09-14).
Computes PMF, CDF, or quantile (inverse CDF) for the Poisson distribution given a rate parameter λ and a count or probability value.
Price / call$0.004
Success—
StatusUnknown
How this service works
Poisson distribution with rate `lambda` (> 0, ≤ 1e9). `function` selects the mass (pmf), cumulative distribution (cdf) or quantile / inverse-CDF.
Output
Returns a single numeric value: either the probability mass (PMF), the cumulative probability (CDF), or the smallest integer k such that CDF(k) ≥ p (quantile), for the specified Poisson distribution parameters.
Example use cases
Rare event probability in operations
“We expect on average 4 customer complaints per day. What is the probability we get exactly 6 complaints tomorrow? Use the Poisson PMF with lambda 4 and k 6.”
Cumulative arrival rate analysis
“If a server receives on average 10 requests per second, what is the probability of receiving 12 or fewer requests in any given second? Compute the Poisson CDF with lambda 10 and x 12.”
Quantile threshold for capacity planning
“Our call center handles Poisson-distributed calls with an average rate of 8 per hour. What call volume corresponds to the 99th percentile so we can plan staffing? Use the Poisson quantile function with lambda 8 and p 0.99.”
Technical details
Endpoint
POSThttps://distribution.openverbs.com/v1/poissonWhen to prefer
Choose this endpoint when you need fast, on-demand computation of Poisson distribution probabilities or quantiles without setting up a statistics library or runtime environment. Ideal for agents performing probabilistic reasoning about count-based events (arrivals, failures, defects) in real time. Prefer this over a generic math API when you specifically need Poisson PMF, CDF, or inverse CDF evaluated server-side with a simple HTTP call.
Side effects
- Invalid λ ≤ 0 returns a validation error
- Probability p outside (0,1) for quantile function returns an error
- Non-integer or negative k for PMF/CDF may return an error or unexpected result
- Missing required fields (function, x, lambda) returns a schema validation error
- Payment failure via x402 protocol prevents access
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| inputrequired | object |
Tags
x402
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