# 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: 2026-05-30T20:18:09.608Z ### 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 No related content is currently linked to this product. ## Integration Details ### 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 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 ` ```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. ### 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). ### 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 ", "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: > Call the AgentPMT-Tool-Search-and-Execution tool with action 'get\_schema' and tool\_id 68b648923c0101597b3cd884 ("Quantum Distribution Generator"). Then call the same tool with action 'call\_tool', tool\_id 68b648923c0101597b3cd884, and the parameters needed for my request. 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.