# 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
- 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: 2026-07-14T22:08:16.254Z

### 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

### 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

#### Quantum Distribution Generator, Product Announcement

- Type: article
- Page URL: https://www.agentpmt.com/articles/quantum-distribution-generator-product-announcement
- Markdown URL: https://www.agentpmt.com/articles/quantum-distribution-generator-product-announcement?format=agent-md
The Quantum Distribution Generator brings statistical sampling and Monte Carlo simulation to the AgentPMT marketplace as a callable connector, so risk, reliability, and clinical-trial models run automatically inside agentic workflows instead of by hand in notebooks.

## Integration Details

### DynamicMCP

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

Use the local router for command-based MCP clients. It forwards requests to `https://api.agentpmt.com/mcp` and does not execute tools locally.

```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

Autonomous agents can access this tool through AgentAddress credit balances or direct x402 payments. Use the Autonomous Agent API reference for endpoint shapes after choosing the access pattern below.

- Autonomous Agent API reference URL: https://www.agentpmt.com/docs/api-reference/autonomous-agents
- Autonomous Agent API reference markdown URL: https://www.agentpmt.com/docs/api-reference/autonomous-agents?format=agent-md
- Credit-Based Access Using AgentAddress: https://www.agentpmt.com/docs/autonomous-agents/credit-based-tool-usage-with-agentaddress
- AgentAddress is preferred for persistent file access, stored platform state, and maximum tool use ability across repeated calls.
- Direct x402 is for independent one-off tool calls that do not require shared files or stored platform state.
- Direct x402 public payments: USDC on Base, Arbitrum, Optimism, Polygon, and Avalanche.

#### Product Skill Package

This product has a published Agent Skill package for product-specific operating instructions.

- Skill slug: quantum-distribution-generator
- Version: 1.0.1
- Download SKILL.md: https://raw.githubusercontent.com/AgentPMT/agent-skills/main/skills/quantum-distribution-generator/SKILL.md
- Package source: https://github.com/AgentPMT/agent-skills/tree/main/skills/quantum-distribution-generator
- OpenClaw listing: https://clawhub.ai/agentpmt/quantum-distribution-generator
- OpenClaw install: `openclaw skills install quantum-distribution-generator`
- skills.sh install: `npx skills add AgentPMT/agent-skills --skill quantum-distribution-generator`
- Last published: 2026-06-29T20:14:01.667Z

### 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
        }
      }
    }
  }
}
```

### Usage Instructions

# Quantum Distribution Generator

Generate statistical distribution samples, Monte Carlo samples, and random walks. Use the product action name in `action`; the backend also accepts legacy `operation` for compatibility.

## Actions

### exponential
Required: `action:"exponential"`.
Optional: `source:"quantum"|"standard"` default `quantum`, `count` 1-10000 default 1, `rate` > 0 default 1.0.
Example: `{"action":"exponential","count":5,"rate":2.5}`

### poisson
Required: `action:"poisson"`.
Optional: `source`, `count` default 1, `lambda_param` > 0 default 1.0. Quantum source max count: 200.
Example: `{"action":"poisson","count":10,"lambda_param":4.5}`

### binomial
Required: `action:"binomial"`.
Optional: `source`, `count`, `n_trials` default 10, `p_success` 0-1 default 0.5. Quantum source max count 200 and max n_trials 50.
Example: `{"action":"binomial","count":20,"n_trials":10,"p_success":0.3}`

### beta
Required: `action:"beta"`.
Optional: `source`, `count`, `alpha` > 0 default 1.0, `beta_param` > 0 default 1.0.
Example: `{"action":"beta","count":10,"alpha":2.0,"beta_param":5.0}`

### gamma
Required: `action:"gamma"`.
Optional: `source`, `count`, `shape` > 0 default 1.0, `scale` > 0 default 1.0.
Example: `{"action":"gamma","count":15,"shape":2.0,"scale":1.5}`

### montecarlo_sample
Required: `action:"montecarlo_sample"`.
Optional: `source`, `samples` 1-1000000 default 1000, `dimensions` 1-100 default 1, `distribution_type:"uniform"|"normal"` default `uniform`.
Example: `{"action":"montecarlo_sample","samples":500,"dimensions":3,"distribution_type":"normal"}`

### randomwalk
Required: `action:"randomwalk"`.
Optional: `source`, `steps` 1-10000 default 100, `dimensions` 1-100 default 1, `step_size` > 0 default 1.0. Quantum source max steps: 80.
Example: `{"action":"randomwalk","steps":50,"dimensions":2,"step_size":0.5}`

### Frequently Asked Questions

#### How do I connect this tool to an external agent?

- Page URL: https://www.agentpmt.com/faq
- Markdown URL: https://www.agentpmt.com/faq?format=agent-md

You can install the local MCP server by opening a terminal and running:

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

This will connect you to local agents like Claude Code, Windsurf, Grok Build, Cursor, etc.

Alternatively you can connect to the hosted version with this config block, no installation required:

```
{
  "mcpServers": {
    "agentpmt": {
      "type": "streamable-http",
      "url": "https://api.agentpmt.com/mcp",
      "headers": {
        "Authorization": "Bearer <AGENTPMT_BEARER_TOKEN>",
        "x-instance-metadata": "{\"client\":\"generic-mcp\",\"platform\":\"remote\"}"
      }
    }
  }
}
```

[View MCP Connection Instructions](/docs/mcp-reference/connection) for more details.

#### How does an external agent use this tool?

- Page URL: https://www.agentpmt.com/faq
- Markdown URL: https://www.agentpmt.com/faq?format=agent-md

After the external agent is connected to an Agent Group that can use this tool, paste this prompt into the agent:

> Use the AgentPMT-Tool-Search-and-Execution tool. First call action 'get\_instructions' so you know how to use the tool search interface. Then call action 'get\_schema' with tool\_id 68b648923c0101597b3cd884 ("Quantum Distribution Generator"). After reading the schema and any returned instructions, tell me what this tool can do, we are going to be using it

The agent should fetch the tool schema first, collect the required parameters for your request, and then call the tool through AgentPMT.

### Dependencies

This product has no public dependency products.