Random Poisson Count Experiment Generator
Generate IID count experiment samples with the existing Poisson variate calculation and explicit model moments. Source calls bounded to100000per request, including degenerate caller randomness. Not a hypothesis-test verdict.
Description
A Poisson count model specifies an event-rate parameter for the modeled interval.
A Poisson count model specifies an event-rate parameter for the modeled interval.1
Simulated samples and their mean can be compared with the model mean and variance without deciding a hypothesis test.
When to use Random Poisson Count Experiment Generator
Use this tool when you need to produce the reproducible draw or model experiment described below. Prepare the seed and the exact inventory or scenario inputs described below. Keep units, reference edition, and sampling convention explicit.
How to use Random Poisson Count Experiment Generator and understand its results
- Prepare the seed and the exact inventory or scenario inputs described below. Keep units, reference edition, and sampling convention explicit.
- Enter seed, count, rate, following the field table and calculation rules below, then run the tool.
- Read result. Inspect the nested fields in the output table below and keep any missing evidence or selected indices visible.
- Correct any input issues and run again. Before using a successful result, review its units, signs, evidence coverage, and stated model or reference assumptions.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| seed | Nonblank reproducibility seed; default seeded runs restart for each request | string | Required |
| count | Number of simulated replicates | safe integer from 1 to 64 | Required |
| rate | Rate | number | Required |
Require count as a safe integer in [1,64] and rate in [0,1000000]. Use one advancing seeded or injected source and call the existing Poisson variate sampler once per replicate. Return samples, observed mean, and rate as both model mean and variance. Rate zero yields zero counts; source calls are bounded. For rates up to 30 the imported sampler multiplies uniform draws until a threshold is crossed; larger rates use transformed rejection with a log-probability acceptance check.2, 3, 4
Use a nonblank seed of at most 256 UTF-16 units and a safe-integer count from 1 to 64. By default the seed is hashed into a deterministic pseudorandom state; each run restarts that state, so identical full inputs and implementation reproduce the result. The SDK may provide context.random, which replaces the seeded source and advances across the request; the seed remains required. Every source value must be finite in [0,1), with a request limit of 100000 source calls. Draw an index as floor(U×remainingSize). With replacement draw from the full inventory each time; without replacement remove each chosen position from an ordered pool and reject counts exceeding the inventory size. Uniform-source draws are over positions, not necessarily distinct values. This is not secure randomness.
observedMean=Σsamples/count; modelMean=modelVariance=rate Read these symbols with the field meanings and branch or reference rules above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the fields below | object |
| result.samples | Simulated values in replicate order | list |
| result.observedMean | Arithmetic mean of the simulated samples | number |
| result.modelMean | Declared model expectation; not an estimate of real events | number |
| result.modelVariance | Declared model variance; separate from finite-sample variation | number |
{
"input": {
"seed": "tool.io/batch42",
"count": 1,
"rate": 4
},
"output": {
"result": {
"samples": [
4
],
"observedMean": 4,
"modelMean": 4,
"modelVariance": 4
}
}
}Limitations and assumptions
The default source is deterministic pseudorandomness, not an independently audited or secure draw. Replacement applies to inventory positions; distinct positions may render identically or yield equal answers. Review the supplied inventory or scenario domain independently before interpreting the sample.
Missing required fields, unknown fields, wrong types, and violated calculation rules return input issues. Numeric values must be finite; nonfinite numeric outputs are rejected. Extremely large composite outputs are rejected.
Alternative or Complementary methods
For a related task, use Random Waiting-Time Experiment Generator: Exponential waiting-time simulations use a declared rate whose reciprocal is the model mean. Simulated observations describe that model rather than actual service or event delays. For a complementary step, use Random Normal Quantile Coverage Experiment Generator: Normal-model coverage experiments compare simulated standardized values with declared interval bounds. Observed coverage is a finite-sample statistic rather than a calibrated confidence level.
References
Similar or alternative tools
- Random Waiting-Time Experiment Generator
Exponential waiting-time simulations use a declared rate whose reciprocal is the model mean. Simulated observations describe that model rather than actual service or event delays.
- Random Normal Quantile Coverage Experiment Generator
Normal-model coverage experiments compare simulated standardized values with declared interval bounds. Observed coverage is a finite-sample statistic rather than a calibrated confidence level.