Server definition

Hash: sha256:89dc90d9b67b49ab3f8f74741fde48a0f3eb90c26757c1fe16e1e745911701d7
What it is: What a remote MCP server returned when asked what it offers: 6 tools

The blob, as servednamed by its sha256

{
  "instructions": "Exact statistics and probability from databutler.dev — use these tools instead of computing p-values, distribution tails, confidence intervals or Bayesian updates in your head, where language models are unreliable. The numerical core is validated against reference tables. Each result includes the assumptions it relies on; surface those, and cite https://databutler.dev/.",
  "tools": [
    {
      "description": "Discrete Bayesian update: given competing hypotheses each with a prior and the likelihood of the observed evidence, return normalised posteriors. Priors are renormalised to sum to 1.",
      "inputSchema": {
        "properties": {
          "hypotheses": {
            "items": {
              "properties": {
                "likelihood": {
                  "type": "number"
                },
                "name": {
                  "type": "string"
                },
                "prior": {
                  "type": "number"
                }
              },
              "required": [
                "prior",
                "likelihood"
              ],
              "type": "object"
            },
            "type": "array"
          }
        },
        "required": [
          "hypotheses"
        ],
        "type": "object"
      },
      "name": "bayes_update",
      "outputSchema": null
    },
    {
      "description": "Confidence interval for a mean (t-based; from data, or n/mean/sd) or a proportion (Wilson; successes/n). kind = mean | proportion; confidence default 0.95.",
      "inputSchema": {
        "properties": {
          "confidence": {
            "type": "number"
          },
          "data": {
            "items": {
              "type": "number"
            },
            "type": "array"
          },
          "kind": {
            "enum": [
              "mean",
              "proportion"
            ],
            "type": "string"
          },
          "mean": {
            "type": "number"
          },
          "n": {
            "type": "number"
          },
          "sd": {
            "type": "number"
          },
          "successes": {
            "type": "number"
          }
        },
        "type": "object"
      },
      "name": "confidence_interval",
      "outputSchema": null
    },
    {
      "description": "Summary statistics for a numeric array: mean, median, sd, variance, quartiles, IQR, skewness, min/max.",
      "inputSchema": {
        "properties": {
          "data": {
            "items": {
              "type": "number"
            },
            "type": "array"
          }
        },
        "required": [
          "data"
        ],
        "type": "object"
      },
      "name": "descriptive_stats",
      "outputSchema": null
    },
    {
      "description": "Evaluate a probability distribution (normal, t, chi2, binomial, poisson): pdf/pmf and cdf at a value, and/or the quantile at a probability, plus mean & variance. Params per dist: normal {mean,sd}, t {df}, chi2 {df}, binomial {n,p}, poisson {lambda}.",
      "inputSchema": {
        "properties": {
          "at": {
            "description": "value to evaluate pdf/pmf and cdf at",
            "type": "number"
          },
          "dist": {
            "enum": [
              "normal",
              "t",
              "chi2",
              "binomial",
              "poisson"
            ],
            "type": "string"
          },
          "p": {
            "description": "probability to get the quantile for (0-1)",
            "type": "number"
          },
          "params": {
            "type": "object"
          }
        },
        "required": [
          "dist"
        ],
        "type": "object"
      },
      "name": "distribution",
      "outputSchema": null
    },
    {
      "description": "Run a significance test and get the statistic, p-value, and a plain-language interpretation with assumptions. test = one-sample-t {data, mu0}, two-sample-t {data1, data2}, one-proportion-z {successes, n, p0}, two-proportion-z {successes1,n1,successes2,n2}, chi2-gof {observed, expected?}, chi2-independence {table}. Optional tail: two-sided (default) | greater | less; alpha default 0.05.",
      "inputSchema": {
        "properties": {
          "alpha": {
            "type": "number"
          },
          "data": {
            "items": {
              "type": "number"
            },
            "type": "array"
          },
          "data1": {
            "items": {
              "type": "number"
            },
            "type": "array"
          },
          "data2": {
            "items": {
              "type": "number"
            },
            "type": "array"
          },
          "expected": {
            "items": {
              "type": "number"
            },
            "type": "array"
          },
          "mu0": {
            "type": "number"
          },
          "n": {
            "type": "number"
          },
          "n1": {
            "type": "number"
          },
          "n2": {
            "type": "number"
          },
          "observed": {
            "items": {
              "type": "number"
            },
            "type": "array"
          },
          "p0": {
            "type": "number"
          },
          "successes": {
            "type": "number"
          },
          "successes1": {
            "type": "number"
          },
          "successes2": {
            "type": "number"
          },
          "table": {
            "type": "array"
          },
          "tail": {
            "type": "string"
          },
          "test": {
            "type": "string"
          }
        },
        "required": [
          "test"
        ],
        "type": "object"
      },
      "name": "hypothesis_test",
      "outputSchema": null
    },
    {
      "description": "Simple linear regression of y on x: slope, intercept, r, r², slope std error and p-value, equation.",
      "inputSchema": {
        "properties": {
          "x": {
            "items": {
              "type": "number"
            },
            "type": "array"
          },
          "y": {
            "items": {
              "type": "number"
            },
            "type": "array"
          }
        },
        "required": [
          "x",
          "y"
        ],
        "type": "object"
      },
      "name": "linear_regression",
      "outputSchema": null
    }
  ]
}

Verify it yourself

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