quantum-distribution-generator

# Quantum Distribution Generator ## Freshness Last updated: `2026-06-29`. If the current date is more than 7 days after the last updated date, reinstall this skill from skills.sh or ClawHub before relying on endpoints, schemas, setup steps, or examples. ## What This Tool Does 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. ## Product 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}` ## When To Use - Use this skill for `Quantum Distribution Generator` on AgentPMT. - Use it when an agent needs this specific tool's behavior, schema, inputs, outputs, and invocation shape. - Search and activation keywords: quantum distribution generator, 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, beta, source, count. - Supported action names: `beta`, `binomial`, `exponential`, `gamma`, `montecarlo_sample`, `poisson`, `randomwalk`. ## 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. ## Categories And Industries No categories or industry tags are published for this tool. ## Actions And Schema Complete generated action schema: `./schema.md`. Supported action count: `7`. x402 availability: not enabled for this product. - `beta` (action slug: `beta`): Generate values from a beta distribution, useful for modeling probabilities and proportions. Price: `5` credits. Parameters: `alpha`, `beta_param`, `count`, `source`. - `binomial` (action slug: `binomial`): Generate values from a binomial distribution, modeling the number of successes in a fixed number of trials. Price: `5` credits. Parameters: `count`, `n_trials`, `p_success`, `source`. - `exponential` (action slug: `exponential`): Generate values from an exponential distribution, commonly used for modeling wait times and decay processes. Price: `5` credits. Parameters: `count`, `rate`, `source`. - `gamma` (action slug: `gamma`): Generate values from a gamma distribution, used for modeling wait times and skewed data. Price: `5` credits. Parameters: `count`, `scale`, `shape`, `source`. - `montecarlo_sample` (action slug: `montecarlo-sample`): Generate multi-dimensional Monte Carlo samples from uniform or normal distributions for simulation and analysis. Price: `5` credits. Parameters: `dimensions`, `distribution_type`, `samples`, `source`. - `poisson` (action slug: `poisson`): Generate values from a Poisson distribution, used for modeling count-based events (e.g., arrivals per hour). Price: `5` credits. Parameters: `count`, `lambda_param`, `source`. - `randomwalk` (action slug: `randomwalk`): Simulate a random walk in one or more dimensions starting from the origin. Quantum max 80 steps. Price: `5` credits. Parameters: `dimensions`, `source`, `step_size`, `steps`. ## Live Schema And Examples Use the compact schema above for ordinary calls. Before a new production integration, or whenever parameters, enum values, nested objects, outputs, or examples are unclear, fetch live details first. - Exact schema: call `agentpmt-tool-search-and-execution` with `action: "get_schema"`, and `tool_id: "quantum-distribution-generator"`. - Detailed examples: call `agentpmt-tool-search-and-execution` with `action: "get_instructions"` and `tool_id: "quantum-distribution-generator"`, or call this product with `action: "get_instructions"` when the product tool is already selected. - Treat returned live schema and instructions as more specific than this generated summary. MCP schema lookup through the main AgentPMT MCP server: ```json { "method": "tools/call", "params": { "name": "AgentPMT-Tool-Search-and-Execution", "arguments": { "action": "get_schema", "tool_id": "quantum-distribution-generator" } } } ``` For live examples, keep the same MCP tool and use these arguments: ```json { "action": "get_instructions", "tool_id": "quantum-distribution-generator" } ``` Authenticated AgentPMT REST schema lookup body: ```json { "name": "agentpmt-tool-search-and-execution", "parameters": { "action": "get_schema", "tool_id": "quantum-distribution-generator" } } ``` Authenticated AgentPMT REST live examples body: ```json { "name": "agentpmt-tool-search-and-execution", "parameters": { "action": "get_instructions", "tool_id": "quantum-distribution-generator" } } ``` ## Call This Tool Product slug: `quantum-distribution-generator` Marketplace page: https://www.agentpmt.com/marketplace/quantum-distribution-generator - AgentPMT account route: first use `../agentpmt-account-mcp-rest-api-setup` to connect the main MCP server or REST API for an Agent Group where this tool is enabled. - x402 route: not enabled for this product. - AgentPMT overview: use `../what-is-agentpmt` for marketplace, Agent Group, workflow, MCP, REST, and payment concepts. If those setup skills are not installed beside this product skill, use the downloads below. Core AgentPMT setup skills: - What AgentPMT is: ../what-is-agentpmt - ClawHub page: https://clawhub.ai/agentpmt/what-is-agentpmt - OpenClaw install: `openclaw skills install what-is-agentpmt` - skills.sh install: `npx skills add AgentPMT/agent-skills --skill what-is-agentpmt` - AgentPMT account MCP/REST setup: ../agentpmt-account-mcp-rest-api-setup - ClawHub page: https://clawhub.ai/agentpmt/agentpmt-account-mcp-rest-api-setup - OpenClaw install: `openclaw skills install agentpmt-account-mcp-rest-api-setup` - skills.sh install: `npx skills add AgentPMT/agent-skills --skill agentpmt-account-mcp-rest-api-setup` skills.sh install script: ```bash npx skills add AgentPMT/agent-skills --skill what-is-agentpmt npx skills add AgentPMT/agent-skills --skill agentpmt-account-mcp-rest-api-setup ``` MCP call shape after the main AgentPMT MCP server is connected: ```json { "method": "tools/call", "params": { "name": "Quantum-Distribution-Generator", "arguments": { "action": "beta", "alpha": 1, "beta_param": 1, "count": 1, "source": "quantum" } } } ``` Use the exact tool name returned by `tools/list`; the name above is the expected readable form. Authenticated AgentPMT REST call body: ```json { "name": "quantum-distribution-generator", "parameters": { "action": "beta", "alpha": 1, "beta_param": 1, "count": 1, "source": "quantum" } } ``` Use the setup skill for the account connection details before making REST calls. ## Response Handling - Treat the returned JSON as the source of truth for this tool call. - If the response includes warnings or correction targets, apply them before retrying. - If the response includes a `passed` or success-style boolean, use it as the workflow gate. - If validation fails or the response shape is unclear, call `get_schema` or `get_instructions` before retrying. - If `beta` fails, preserve the request parameters and retry only after fixing schema, auth, or payment errors. ## Security - Do not place account secrets, wallet private keys, mnemonics, signatures, or payment headers in prompts or logs. - Keep tool inputs scoped to the minimum content needed for the task. - Use the setup skills for credential handling; this product skill only defines product-specific behavior. ## AgentPMT Reference - What AgentPMT is: ../what-is-agentpmt (ClawHub: `what-is-agentpmt`, page: https://clawhub.ai/agentpmt/what-is-agentpmt; skills.sh: `npx skills add AgentPMT/agent-skills --skill what-is-agentpmt`) - AgentPMT account MCP/REST setup: ../agentpmt-account-mcp-rest-api-setup (ClawHub: `agentpmt-account-mcp-rest-api-setup`, page: https://clawhub.ai/agentpmt/agentpmt-account-mcp-rest-api-setup; skills.sh: `npx skills add AgentPMT/agent-skills --skill agentpmt-account-mcp-rest-api-setup`) - Marketplace product: https://www.agentpmt.com/marketplace/quantum-distribution-generator - AgentPMT main MCP server: https://api.agentpmt.com/mcp/ - AgentPMT REST invoke endpoint: https://api.agentpmt.com/products/purchase