# Quantum Distribution Generator

## Links

- Product page URL: https://www.agentpmt.com/marketplace/quantum-distribution-generator
- Product markdown URL: https://www.agentpmt.com/marketplace/quantum-distribution-generator?format=agent-md
- Product JSON URL: https://www.agentpmt.com/marketplace/quantum-distribution-generator?format=agent-json

## Overview

- Product ID: 68b648923c0101597b3cd884
- Vendor: Apoth3osis
- Type: function
- Unit type: request
- Price: 500 credits
- Categories: Quantum Randomness & Entropy, Statistical Distributions (Quantum), Scientific Computing, Financial Modeling, Quantum Selection & Sampling, Quantum Simulation & Analysis, Quality Assurance
- Generated at: 2026-04-15T18:27:01.981Z

### Page Description

Statistical distribution sampling and stochastic simulation powered by quantum or pseudo-random sources. Generate samples from common probability distributions including exponential, Poisson, binomial, beta, and gamma, with support for Monte Carlo sampling and multi-dimensional random walks. Configurable parameters for distribution shapes, sample counts, and dimensionality enable flexible statistical modeling and simulation workflows.

### Agent Description

Sample from probability distributions (exponential, Poisson, binomial, beta, gamma) with Monte Carlo and random walk simulation support.

## Details Tab

### Details

Statistical distribution sampling and stochastic simulation powered by quantum or pseudo-random sources. Generate samples from common probability distributions including exponential, Poisson, binomial, beta, and gamma, with support for Monte Carlo sampling and multi-dimensional random walks. Configurable parameters for distribution shapes, sample counts, and dimensionality enable flexible statistical modeling and simulation workflows.

### Actions

- `exponential` (5 credits): Generate values from an exponential distribution, commonly used for modeling wait times and decay processes.
- `poisson` (5 credits): Generate values from a Poisson distribution, used for modeling count-based events (e.g., arrivals per hour).
- `binomial` (5 credits): Generate values from a binomial distribution, modeling the number of successes in a fixed number of trials.
- `beta` (5 credits): Generate values from a beta distribution, useful for modeling probabilities and proportions.
- `gamma` (5 credits): Generate values from a gamma distribution, used for modeling wait times and skewed data.
- `montecarlo_sample` (5 credits): Generate multi-dimensional Monte Carlo samples from uniform or normal distributions for simulation and analysis.
- `randomwalk` (5 credits): Simulate a random walk in one or more dimensions starting from the origin. Quantum max 80 steps.

### Use Cases

Monte Carlo simulations for risk analysis and option pricing, queuing theory modeling with Poisson and exponential distributions, A/B testing and conversion rate analysis using binomial and beta distributions, stochastic process simulation, particle diffusion and Brownian motion modeling, Bayesian inference and prior distribution sampling, financial market random walk simulations, statistical hypothesis testing, reliability engineering and failure time analysis.

### Workflows Using This Tool

No public workflows currently reference this product.

### Related Content

No related content is currently linked to this product.

## Advanced Tab

### DynamicMCP

- Setup page URL: https://www.agentpmt.com/dynamic-mcp
- Claude setup guide: https://www.agentpmt.com/dynamic-mcp?platform=claude#videos
- ChatGPT setup guide: https://www.agentpmt.com/dynamic-mcp?platform=chatgpt#videos
- Cursor setup guide: https://www.agentpmt.com/dynamic-mcp?platform=cursor#videos
- Windsurf setup guide: https://www.agentpmt.com/dynamic-mcp?platform=windsurf#videos

STDIO connector for Claude Code, Codex, Cursor, Zed, and other LLMs that require STDIO or custom connections. This lightweight connector routes requests to `https://api.agentpmt.com/mcp`. All tool execution happens in the cloud and the server cannot edit any files on your computer.

```bash
npm install -g @agentpmt/mcp-router
agentpmt-setup
```

### REST API

The live page renders cURL, Python, JavaScript, and Node.js examples. Logged-in users see those examples prefilled with their own API and budget credentials.

- Purchase endpoint: https://api.agentpmt.com/products/purchase
- Authorization format: `Bearer <base64(apiKey:budgetKey)>`

```bash
curl -X POST "https://api.agentpmt.com/products/purchase" \
  -H "Content-Type: application/json" \
  -H "Authorization: Bearer eW91ci1hcGkta2V5LWhlcmU6eW91ci1idWRnZXQta2V5LWhlcmU=" \
  -d '{
    "product_id": "68b648923c0101597b3cd884",
    "parameters": {
      "action": "exponential",
      "source": "quantum",
      "count": 1,
      "rate": 1
    }
  }'
```

### Autonomous Agents

Do not use the abbreviated instructions in this product markdown for wallet-based invocation. Retrieve the full External Agent API markdown document instead.

- External Agent API page URL: https://www.agentpmt.com/external-agent-api
- External Agent API markdown URL: https://www.agentpmt.com/external-agent-api?format=agent-md

### Schema

#### Parameters

- Schema type: actions

```json
{
  "actions": {
    "exponential": {
      "description": "Generate values from an exponential distribution, commonly used for modeling wait times and decay processes.",
      "properties": {
        "source": {
          "type": "string",
          "description": "Random source: 'quantum' (default) or 'standard'.",
          "required": false,
          "default": "quantum",
          "enum": [
            "quantum",
            "standard"
          ]
        },
        "count": {
          "type": "integer",
          "description": "Number of values to generate (1-10000).",
          "required": false,
          "default": 1,
          "minimum": 1,
          "maximum": 10000
        },
        "rate": {
          "type": "number",
          "description": "Rate parameter (lambda), must be > 0.",
          "required": false,
          "default": 1
        }
      }
    },
    "poisson": {
      "description": "Generate values from a Poisson distribution, used for modeling count-based events (e.g., arrivals per hour).",
      "properties": {
        "source": {
          "type": "string",
          "description": "Random source: 'quantum' or 'standard'. Quantum max count: 200.",
          "required": false,
          "default": "quantum",
          "enum": [
            "quantum",
            "standard"
          ]
        },
        "count": {
          "type": "integer",
          "description": "Number of values to generate (1-10000, quantum max 200).",
          "required": false,
          "default": 1,
          "minimum": 1,
          "maximum": 10000
        },
        "lambda_param": {
          "type": "number",
          "description": "Expected rate (lambda), must be > 0.",
          "required": false,
          "default": 1
        }
      }
    },
    "binomial": {
      "description": "Generate values from a binomial distribution, modeling the number of successes in a fixed number of trials.",
      "properties": {
        "source": {
          "type": "string",
          "description": "Random source: 'quantum' or 'standard'. Quantum limits: max 200 count, max 50 trials.",
          "required": false,
          "default": "quantum",
          "enum": [
            "quantum",
            "standard"
          ]
        },
        "count": {
          "type": "integer",
          "description": "Number of values to generate (1-10000, quantum max 200).",
          "required": false,
          "default": 1,
          "minimum": 1,
          "maximum": 10000
        },
        "n_trials": {
          "type": "integer",
          "description": "Number of trials per sample (1-10000, quantum max 50).",
          "required": false,
          "default": 10,
          "minimum": 1,
          "maximum": 10000
        },
        "p_success": {
          "type": "number",
          "description": "Probability of success per trial (0-1).",
          "required": false,
          "default": 0.5,
          "minimum": 0,
          "maximum": 1
        }
      }
    },
    "beta": {
      "description": "Generate values from a beta distribution, useful for modeling probabilities and proportions.",
      "properties": {
        "source": {
          "type": "string",
          "description": "Random source: 'quantum' or 'standard'. Quantum max count: 50.",
          "required": false,
          "default": "quantum",
          "enum": [
            "quantum",
            "standard"
          ]
        },
        "count": {
          "type": "integer",
          "description": "Number of values to generate (1-10000, quantum max 50).",
          "required": false,
          "default": 1,
          "minimum": 1,
          "maximum": 10000
        },
        "alpha": {
          "type": "number",
          "description": "Alpha shape parameter, must be > 0.",
          "required": false,
          "default": 1
        },
        "beta_param": {
          "type": "number",
          "description": "Beta shape parameter, must be > 0.",
          "required": false,
          "default": 1
        }
      }
    },
    "gamma": {
      "description": "Generate values from a gamma distribution, used for modeling wait times and skewed data.",
      "properties": {
        "source": {
          "type": "string",
          "description": "Random source: 'quantum' or 'standard'. Quantum max count: 75.",
          "required": false,
          "default": "quantum",
          "enum": [
            "quantum",
            "standard"
          ]
        },
        "count": {
          "type": "integer",
          "description": "Number of values to generate (1-10000, quantum max 75).",
          "required": false,
          "default": 1,
          "minimum": 1,
          "maximum": 10000
        },
        "shape": {
          "type": "number",
          "description": "Shape parameter, must be > 0.",
          "required": false,
          "default": 1
        },
        "scale": {
          "type": "number",
          "description": "Scale parameter, must be > 0.",
          "required": false,
          "default": 1
        }
      }
    },
    "montecarlo_sample": {
      "description": "Generate multi-dimensional Monte Carlo samples from uniform or normal distributions for simulation and analysis.",
      "properties": {
        "source": {
          "type": "string",
          "description": "Random source: 'quantum' or 'standard'.",
          "required": false,
          "default": "quantum",
          "enum": [
            "quantum",
            "standard"
          ]
        },
        "samples": {
          "type": "integer",
          "description": "Number of samples to generate (1-1000000).",
          "required": false,
          "default": 1000,
          "minimum": 1,
          "maximum": 1000000
        },
        "dimensions": {
          "type": "integer",
          "description": "Number of dimensions per sample (1-100).",
          "required": false,
          "default": 1,
          "minimum": 1,
          "maximum": 100
        },
        "distribution_type": {
          "type": "string",
          "description": "Distribution for sampling: 'uniform' or 'normal'.",
          "required": false,
          "default": "uniform",
          "enum": [
            "uniform",
            "normal"
          ]
        }
      }
    },
    "randomwalk": {
      "description": "Simulate a random walk in one or more dimensions starting from the origin. Quantum max 80 steps.",
      "properties": {
        "source": {
          "type": "string",
          "description": "Random source: 'quantum' or 'standard'. Quantum max steps: 80.",
          "required": false,
          "default": "quantum",
          "enum": [
            "quantum",
            "standard"
          ]
        },
        "steps": {
          "type": "integer",
          "description": "Number of steps (1-10000, quantum max 80).",
          "required": false,
          "default": 100,
          "minimum": 1,
          "maximum": 10000
        },
        "dimensions": {
          "type": "integer",
          "description": "Number of dimensions (1-100).",
          "required": false,
          "default": 1,
          "minimum": 1,
          "maximum": 100
        },
        "step_size": {
          "type": "number",
          "description": "Size of each step, must be > 0.",
          "required": false,
          "default": 1
        }
      }
    }
  },
  "properties": {}
}
```

### Usage Instructions

# 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:**
```json
{
  "operation": "exponential",
  "count": 5,
  "rate": 2.5
}
```

---

### 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:**
```json
{
  "operation": "poisson",
  "count": 10,
  "lambda_param": 4.5
}
```

---

### 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:**
```json
{
  "operation": "binomial",
  "count": 20,
  "n_trials": 10,
  "p_success": 0.3
}
```

---

### 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:**
```json
{
  "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:**
```json
{
  "operation": "gamma",
  "count": 15,
  "shape": 2.0,
  "scale": 1.5
}
```

---

### 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:**
```json
{
  "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:**
```json
{
  "operation": "randomwalk",
  "steps": 50,
  "dimensions": 2,
  "step_size": 0.5
}
```

---

## 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.

---

## 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).

### About The Developer

- Vendor name: Apoth3osis
- Website: apoth3osis.io

We build tools that enable AI agents to excel in the mathematical realm.

Our small team develops experimental and unique solutions in the AI arena, with a strong focus on modular computing for agentic applications and custom model deployment. We have handled projects for a variety of applications across many sectors, from algorithmic trading and financial analysis, to molecular simulations and predictions, to habitat and biodiversity monitoring and wildlife conservation.

### Frequently Asked Questions

No linked FAQs are currently available.

### Dependencies

This product has no public dependency products.