Random Uncertainty Band Chart Dataset Generator

Description

Generate synthetic lower and upper chart bands using independent nonnegative widths around supplied centers, without confidence-interval inference.

A chart dataset contains values plus the labels, grouping, totals, or missing-value conventions needed to interpret them. Separating the numeric construction from plotting makes conservation rules and deliberate edge cases visible before a chart is rendered.

Generate synthetic lower and upper chart bands using independent nonnegative widths around supplied centers, without confidence-interval inference.

When to use this tool

Use this generator to create reproducible uncertainty band chart dataset cases from the supplied model or bank. Inspect the returned evidence before using cases in a test or exercise.

How to use the tool and how it works

Supply centers, minimumWidth, maximumWidth in the field shapes below. Set seed when you need an explicit replay.
Run the tool and correct any input error. For generated controls, distinguish a successful fixture containing an invalid case from failure to generate the fixture.
Read centers, lower, upper, minimum, maximum, rule. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.

For each supplied center, independently draw nonnegative integer widths for the lower and upper side. Subtract/add them, return global lower/upper extrema and label the synthetic width rule.^[1]

Delegated operations used for this result: minimum; maximum. Their calculation or parsing conventions apply to the corresponding result fields.^{[2, 3]}

Input field	Meaning and units	Accepted input
centers	Centers	Required. Array of Finite number.; minimum items 1; maximum items 32.
minimumWidth	Minimum Width	Required. Safe integer; minimum 0; maximum 9007199254740990.
maximumWidth	Maximum Width	Required. Safe integer; minimum 0; maximum 9007199254740990.
seed	Optional numeric seed; takes precedence over context randomness. Without either, use the fixed tool.io default seed.	Optional. Safe integer.

Output field	Interpretation	Returned shape
centers	Centers	Required. Array of Finite number.; minimum items 1; maximum items 32.
lower	Lower	Required. Array of Finite number.; minimum items 1; maximum items 32.
upper	Upper	Required. Array of Finite number.; minimum items 1; maximum items 32.
minimum	Minimum	Required. Finite number.
maximum	Maximum	Required. Finite number.
rule	Rule	Required. Text.
randomness	Replay metadata: source is seed or context; seed is the normalized 32-bit seed or null for a context source.	Required. Object; no unknown keys.
randomness.seed	Optional numeric replay seed; normalization and precedence are explained below.	Required. Safe integer. or Null.
randomness.source	Source	Required. Text; one of "context", "seed".

An explicit safe-integer seed takes precedence over injected context randomness and is normalized to an unsigned 32-bit integer. With no seed and no context source, replay uses the fixed tool.io default seed. A context source must return finite values from zero inclusive to one exclusive; its advancing state must be retained separately. randomness records the source and normalized seed, or null for context. These generators are not cryptographic random sources.

json

{
  "input": {
    "centers": [
      10,
      20
    ],
    "minimumWidth": 1,
    "maximumWidth": 3,
    "seed": 42
  },
  "output": {
    "centers": [
      10,
      20
    ],
    "lower": [
      8,
      17
    ],
    "upper": [
      12,
      23
    ],
    "minimum": 8,
    "maximum": 23,
    "rule": "independent uniform integer widths; synthetic, not confidence bounds",
    "randomness": {
      "seed": 42,
      "source": "seed"
    }
  }
}

Limitations and assumptions

The band is not a confidence, prediction or credible interval. Independent side widths can be asymmetric, and plotting order/axis interpretation remains with the caller.
A replay requires the same complete input and implementation. Randomized construction does not guarantee uniform coverage of every feasible output; finite samples can repeat unless a distinct-selection rule is explicitly stated.
The field tables state structural bounds; cross-field constraints and bounded search or output budgets also apply. Unknown keys are rejected where the object contract disallows them. Input errors are distinct from null fields and deliberate invalid controls in a successful output.

Alternative or Complementary methods

For a supplied example, inspect the returned construction or delegated check directly. To evaluate a consumer, also test cases chosen for its own boundaries; a generated finite corpus does not establish exhaustive coverage.

References

Tool behavior and example: Random Uncertainty Band Chart Dataset Generator — tool.io
Calculation or validation: statistics/minimum — tool.io
Calculation or validation: statistics/maximum — tool.io

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