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Normal Distribution Calculator (PDF, CDF, Quantile)
x402
Normal Distribution Calculator (PDF, CDF, Quantile) 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 the probability density function (PDF), cumulative distribution function (CDF), or quantile (inverse CDF) for a normal (Gaussian) distribution given a mean, standard deviation, and evaluation point.
Price / call$0.004
Success—
StatusUnknown
How this service works
Normal distribution with optional mean (default 0) and standard deviation sd (default 1). `function` selects the density (pdf), cumulative distribution (cdf) or quantile / inverse-CDF.
Output
Returns a numeric result corresponding to the requested function: a probability density value (PDF), a cumulative probability between 0 and 1 (CDF), or a variate value (quantile/inverse CDF) for the given normal distribution parameters.
Example use cases
Z-score significance test
“I need to know the two-tailed p-value for a z-score of 2.33 — can you give me the CDF of a standard normal distribution (mean 0, std 1) at x = 2.33?”
IQ percentile lookup
“IQ scores are normally distributed with a mean of 100 and standard deviation of 15. What percentile (CDF) is someone with an IQ of 130?”
Risk threshold quantile
“My model assumes returns are normally distributed with mean 0.05 and standard deviation 0.12. What return value corresponds to the bottom 5th percentile — i.e. the quantile at p = 0.05?”
Technical details
Endpoint
POSThttps://distribution.openverbs.com/v1/normalWhen to prefer
Choose this endpoint when you need fast, on-demand computation of normal distribution statistics (PDF, CDF, or quantile) without setting up a local statistics library. Ideal for AI agents performing probabilistic reasoning, hypothesis testing, or risk analysis that require a single clean API call rather than executing code. Particularly useful in sandboxed environments where running Python or R is not available.
Side effects
- Standard deviation ≤ 0 returns a validation error (schema enforces exclusiveMinimum: 0)
- Quantile called with x outside (0,1) returns an error since p must be a valid probability
- Missing required fields (function or x) returns a 400-level error
- Payment not included or insufficient balance returns a 402 Payment Required response
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| inputrequired | object |
Tags
x402
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