Description
Generate affine floating-point uniform interval samples, histogram counts and delegated population summaries alongside theoretical mean/variance; rounding may attain the upper endpoint and bins include it in the last cell.
Synthetic statistical data separates a specified generating model from the values observed in a finite draw. A model parameter, a sample summary, and the result of a fitted analysis answer different questions; retaining them separately makes numerical and statistical checks easier to interpret.
Generate affine floating-point uniform interval samples, histogram counts and delegated population summaries alongside theoretical mean/variance; rounding may attain the upper endpoint and bins include it in the last cell.
When to use this tool
Use this generator to create reproducible monte carlo uniform 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 count, lowerBound, upperBound, binCount 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 samples, histogram, summary, theoreticalMean, theoreticalVariance. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.
Draw uniform variates scaled to the supplied finite positive-width interval, bin them with a clamped upper-edge bin, and return a population summary alongside theoretical mean and variance span-squared divided by twelve.1
Delegated operations used for this result: population summary. Their calculation or parsing conventions apply to the corresponding result fields.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| count | Requested count; the mechanics explain whether one draw expands into several returned records. | Required. Safe integer; minimum 1; maximum 4096. |
| lowerBound | Lower Bound | Required. Finite number. |
| upperBound | Upper Bound | Required. Finite number. |
| binCount | Bin Count | Required. Safe integer; minimum 1; maximum 64. |
| 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 |
|---|---|---|
| samples | Samples | Required. Array of Finite number.; minimum items 1; maximum items 4096. |
| histogram | Histogram | Required. Array of Safe integer; minimum 0; maximum 4096.; minimum items 1; maximum items 64. |
| summary | Summary | Required. Object; no unknown keys. |
| summary.count | Requested count; the mechanics explain whether one draw expands into several returned records. | Required. Safe integer; minimum 1; maximum 4096. |
| summary.mean | Mean | Required. Finite number. |
| summary.variance | Variance | Required. Finite number; minimum 0. |
| summary.standardDeviation | Standard Deviation | Required. Finite number; minimum 0. |
| theoreticalMean | Theoretical Mean | Required. Finite number. |
| theoreticalVariance | Theoretical Variance | Required. Finite number; minimum 0. |
| 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.
{
"input": {
"count": 5,
"lowerBound": -2,
"upperBound": 4,
"binCount": 3,
"seed": 42
},
"output": {
"samples": [
1.6066225115209818,
0.68974335398525,
3.114794760942459,
2.018404248636216,
-0.9511166075244546
],
"histogram": [
1,
2,
2
],
"summary": {
"count": 5,
"mean": 1.2956896535120905,
"standardDeviation": 1.3670002423275243,
"variance": 1.86868966252351
},
"theoreticalMean": 1,
"theoreticalVariance": 3.0000000000000004,
"randomness": {
"seed": 42,
"source": "seed"
}
}
}Limitations and assumptions
- Binary64 rounding can place a value on the upper bound despite the underlying unit draw being below one. Histograms and finite-sample moments are simulations, not guarantees of exact theoretical agreement.
- 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
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