Description
Simulate exact-count one-dimensional unit-step paths under an explicit forward-step probability, reusing cumulative sums and population endpoint summaries without predicting a real process.
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.
Simulate exact-count one-dimensional unit-step paths under an explicit forward-step probability, reusing cumulative sums and population endpoint summaries without predicting a real process.
When to use this tool
Use this generator to create reproducible monte carlo random walk 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 steps, pathCount, startPosition, positiveStepProbability 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 paths, finalPositions, endpointMean, endpointPopulationVariance. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.
Draw independent plus-one or minus-one increments for each path using positiveStepProbability, delegate cumulative sums, and add startPosition. Return paths including the start and the population mean and variance of final positions.1
Delegated operations used for this result: cumulative sum; population summary. Their calculation or parsing conventions apply to the corresponding result fields.2, 3
| Input field | Meaning and units | Accepted input |
|---|---|---|
| steps | Steps | Required. Safe integer; minimum 1; maximum 1024. |
| pathCount | Exact number of paths; pathCount × (steps + 1) must not exceed 16,384 retained positions. | Required. Safe integer; minimum 1; maximum 32. |
| startPosition | Start Position | Required. Safe integer. |
| positiveStepProbability | Positive Step Probability | Required. Finite number; minimum 0; maximum 1. |
| 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 |
|---|---|---|
| paths | Paths | Required. Array of Array of Safe integer.; minimum items 2; maximum items 1025.; minimum items 1; maximum items 32. |
| finalPositions | Final Positions | Required. Array of Safe integer.; minimum items 1; maximum items 32. |
| endpointMean | Endpoint Mean | Required. Finite number. |
| endpointPopulationVariance | Endpoint Population 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": {
"steps": 6,
"pathCount": 3,
"startPosition": 2,
"positiveStepProbability": 0.5,
"seed": 42
},
"output": {
"paths": [
[
2,
1,
2,
1,
0,
1,
0
],
[
2,
3,
2,
1,
2,
3,
2
],
[
2,
1,
2,
3,
2,
1,
0
]
],
"finalPositions": [
0,
2,
0
],
"endpointMean": 0.6666666666666667,
"endpointPopulationVariance": 0.888888888888889,
"randomness": {
"seed": 42,
"source": "seed"
}
}
}Limitations and assumptions
- Positions must remain safe integers and total stored positions are bounded. This is a discrete one-dimensional walk rather than a fitted physical process or financial forecast.
- 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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