Quantum Distribution Generator

Generate random values from statistical probability distributions and perform Monte Carlo simulations and random walks, powered by quantum or standard randomness sources.

Actions

exponential

Generate values from an exponential distribution, commonly used for modeling wait times and decay processes.

Required Fields:

• operation (string): "exponential"

Optional Fields:

• source (string): Random source — "quantum" (default) or "standard"
• count (integer): Number of values to generate, 1–10000 (default: 1)
• rate (number): Rate parameter, must be > 0 (default: 1.0)

Example:

{
  "operation": "exponential",
  "count": 5,
  "rate": 2.5
}

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poisson

Generate values from a Poisson distribution, used for modeling count-based events (e.g., arrivals per hour).

Required Fields:

• operation (string): "poisson"

Optional Fields:

• source (string): "quantum" (default) or "standard"
• count (integer): Number of values, 1–10000 (default: 1). When using quantum source, max 200.
• lambda_param (number): Expected rate (lambda), must be > 0 (default: 1.0)

Example:

{
  "operation": "poisson",
  "count": 10,
  "lambda_param": 4.5
}

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binomial

Generate values from a binomial distribution, modeling the number of successes in a fixed number of trials.

Required Fields:

• operation (string): "binomial"

Optional Fields:

• source (string): "quantum" (default) or "standard"
• count (integer): Number of values, 1–10000 (default: 1). When using quantum source, max 200.
• n_trials (integer): Number of trials per sample, 1–10000 (default: 10). When using quantum source, max 50.
• p_success (number): Probability of success per trial, 0–1 (default: 0.5)

Example:

{
  "operation": "binomial",
  "count": 20,
  "n_trials": 10,
  "p_success": 0.3
}

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beta

Generate values from a beta distribution, useful for modeling probabilities and proportions.

Required Fields:

• operation (string): "beta"

Optional Fields:

• source (string): "quantum" (default) or "standard"
• count (integer): Number of values, 1–10000 (default: 1). When using quantum source, max 50.
• alpha (number): Alpha shape parameter, must be > 0 (default: 1.0)
• beta (number): Beta shape parameter, must be > 0 (default: 1.0)

Example:

{
  "operation": "beta",
  "count": 10,
  "alpha": 2.0,
  "beta": 5.0
}

---

gamma

Generate values from a gamma distribution, used for modeling wait times and skewed data.

Required Fields:

• operation (string): "gamma"

Optional Fields:

• source (string): "quantum" (default) or "standard"
• count (integer): Number of values, 1–10000 (default: 1). When using quantum source, max 75.
• shape (number): Shape parameter, must be > 0 (default: 1.0)
• scale (number): Scale parameter, must be > 0 (default: 1.0)

Example:

{
  "operation": "gamma",
  "count": 15,
  "shape": 2.0,
  "scale": 1.5
}

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montecarlo_sample

Generate multi-dimensional Monte Carlo samples from uniform or normal distributions.

Required Fields:

• operation (string): "montecarlo_sample"

Optional Fields:

• source (string): "quantum" (default) or "standard"
• samples (integer): Number of samples, 1–1000000 (default: 1000)
• dimensions (integer): Number of dimensions per sample, 1–100 (default: 1)
• distribution (string): "uniform" (default) or "normal"

Example:

{
  "operation": "montecarlo_sample",
  "samples": 500,
  "dimensions": 3,
  "distribution": "normal"
}

---

randomwalk

Simulate a random walk in one or more dimensions, starting from the origin.

Required Fields:

• operation (string): "randomwalk"

Optional Fields:

• source (string): "quantum" (default) or "standard"
• steps (integer): Number of steps, 1–10000 (default: 100). When using quantum source, max 80.
• dimensions (integer): Number of dimensions, 1–100 (default: 1)
• step_size (number): Size of each step, must be > 0 (default: 1.0)

Example:

{
  "operation": "randomwalk",
  "steps": 50,
  "dimensions": 2,
  "step_size": 0.5
}

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Common Workflows

Risk Simulation

Generate exponential or Poisson samples to model event timing and frequency, then use Monte Carlo sampling for multi-factor analysis.

A/B Test Modeling

Use beta distributions to model conversion rate probabilities for two variants, then compare the resulting distributions.

Stock Price Path Simulation

Use randomwalk with dimensions: 1 and an appropriate step_size to simulate asset price movements over time.

Bayesian Parameter Estimation

Combine beta or gamma distributions to sample prior/posterior distributions for parameter estimation tasks.

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Important Notes

• Quantum vs Standard source: The "quantum" source uses true quantum randomness but has lower count/step limits for certain distributions. The "standard" source uses cryptographic randomness and supports the full range of counts.
• Quantum source limits: Poisson max 200 count, Binomial max 200 count and 50 trials, Beta max 50 count, Gamma max 75 count, Random Walk max 80 steps. Use "standard" source for larger quantities.
• All parameters have defaults: Only operation is strictly required for any action. All other parameters fall back to sensible defaults.
• Return format: Each action returns the generated values along with metadata (count, parameters used, source type).