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Probability Distributions – t-Distribution
x402
Probability Distributions – t-Distribution is a paid API for AI agents from distribution.openverbs.com, paid per call via x402, $0.004/call, status unknown (last checked 2026-10-28).
Computes PDF, CDF, or quantile (inverse CDF) for the Student's t-distribution given a value and degrees of freedom
Price / call$0.004
Success—
StatusUnknown
How this service works
Student's t distribution with df degrees of freedom (> 0). `function` selects the density (pdf), cumulative distribution (cdf) or quantile / inverse-CDF.
Output
Returns a numerical result representing either the probability density (PDF), cumulative probability (CDF), or the quantile value (inverse CDF) of the Student's t-distribution for the specified evaluation point and degrees of freedom.
Example use cases
Hypothesis test p-value calculation
“I have a t-statistic of 2.3 with 15 degrees of freedom — can you give me the CDF value of the t-distribution at that point so I can work out the p-value?”
Critical value for confidence interval
“What is the 97.5th percentile (quantile at p=0.975) of the t-distribution with 29 degrees of freedom? I need this for a 95% confidence interval.”
Probability density for model verification
“Can you compute the PDF of the Student's t-distribution at x=0.5 with 5 degrees of freedom so I can verify my stats library is giving the right answer?”
Technical details
Endpoint
POSThttps://distribution.openverbs.com/v1/t?utm_source=zero.xyzWhen to prefer
Choose this endpoint when you need precise numerical evaluation of Student's t-distribution functions (PDF, CDF, or quantile/inverse CDF) for statistical computations such as hypothesis testing, confidence interval construction, or Bayesian inference, especially when you need a lightweight, pay-per-call API rather than running a local stats library.
Side effects
- Invalid degrees of freedom (df ≤ 0) returns a validation error
- For the quantile function, x must be in (0,1); values outside this range return an error
- Missing required fields (function, x, df) return a schema validation error
- Extremely large or small x values may produce numerical precision issues
- Unsupported function enum values return a bad request error
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| x | number | Evaluation point: the variate for pdf/pmf/cdf, or the probability p ∈ (0,1) for quantile. |
| df | number | Degrees of freedom ν > 0. |
| function | string |
Tags
x402
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