Quantum Distribution Generator by Apoth3osis

Name: Quantum Distribution Generator
Brand: Apoth3osis
SKU: 68b648923c0101597b3cd884
Price: 0.05 USD
Availability: InStock

Quantum Distribution Generator

Function

Available ActionsEach successful request consumes credits as outlined below.

exponential^5crpoisson^5crbinomial^5crbeta^5crgamma^5crmontecarlo_sample^5crrandomwalk^5cr

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.

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.

Dynamic MCP Setup

Connect once through AgentPMT Dynamic MCP, then use approved tools from the same agent connection.

30 Second Setup

STDIO connector for Claude Code, Codex, Cursor, Zed, and other LLMs that require STDIO or custom connections.

npm install -g @agentpmt/mcp-routeragentpmt-setup

Hosted Streamable HTTPS

MCP endpoint for browser-based apps like ChatGPT, Claude, Grok, or any time you want a streamable connection with no local install.

https://api.agentpmt.com/mcp

Config Example

Use the hosted endpoint directly in clients that support remote MCP. Store your Bearer token in the client config or secret field.

Full connection guide

{
  "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\"}"
      }
    }
  }
}

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More About Dynamic MCP

Actions(7)

exponential^5cr3 params

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

sourcestring

Random source: 'quantum' (default) or 'standard'.

Values:

quantumstandard

Default: quantum

countinteger

Number of values to generate (1-10000).

Default: 1

Range: 1 - 10000

ratenumber

Rate parameter (lambda), must be > 0.

Default: 1

poisson^5cr3 params

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

sourcestring

Random source: 'quantum' or 'standard'. Quantum max count: 200.

Values:

quantumstandard

Default: quantum

countinteger

Number of values to generate (1-10000, quantum max 200).

Default: 1

Range: 1 - 10000

lambda_paramnumber

Expected rate (lambda), must be > 0.

Default: 1

binomial^5cr4 params

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

sourcestring

Random source: 'quantum' or 'standard'. Quantum limits: max 200 count, max 50 trials.

Values:

quantumstandard

Default: quantum

countinteger

Number of values to generate (1-10000, quantum max 200).

Default: 1

Range: 1 - 10000

n_trialsinteger

Number of trials per sample (1-10000, quantum max 50).

Default: 10

Range: 1 - 10000

p_successnumber

Probability of success per trial (0-1).

Default: 0.5

Range: 0 - 1

beta^5cr4 params

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

sourcestring

Random source: 'quantum' or 'standard'. Quantum max count: 50.

Values:

quantumstandard

Default: quantum

countinteger

Number of values to generate (1-10000, quantum max 50).

Default: 1

Range: 1 - 10000

alphanumber

Alpha shape parameter, must be > 0.

Default: 1

beta_paramnumber

Beta shape parameter, must be > 0.

Default: 1

gamma^5cr4 params

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

sourcestring

Random source: 'quantum' or 'standard'. Quantum max count: 75.

Values:

quantumstandard

Default: quantum

countinteger

Number of values to generate (1-10000, quantum max 75).

Default: 1

Range: 1 - 10000

shapenumber

Shape parameter, must be > 0.

Default: 1

scalenumber

Scale parameter, must be > 0.

Default: 1

montecarlo_sample^5cr4 params

Generate multi-dimensional Monte Carlo samples from uniform or normal distributions for simulation and analysis.

sourcestring

Random source: 'quantum' or 'standard'.

Values:

quantumstandard

Default: quantum

samplesinteger

Number of samples to generate (1-1000000).

Default: 1000

Range: 1 - 1000000

dimensionsinteger

Number of dimensions per sample (1-100).

Default: 1

Range: 1 - 100

distribution_typestring

Distribution for sampling: 'uniform' or 'normal'.

Values:

uniformnormal

Default: uniform

randomwalk^5cr4 params

Simulate a random walk in one or more dimensions starting from the origin. Quantum max 80 steps.

sourcestring

Random source: 'quantum' or 'standard'. Quantum max steps: 80.

Values:

quantumstandard

Default: quantum

stepsinteger

Number of steps (1-10000, quantum max 80).

Default: 100

Range: 1 - 10000

dimensionsinteger

Number of dimensions (1-100).

Default: 1

Range: 1 - 100

step_sizenumber

Size of each step, must be > 0.

Default: 1

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

import requests
import json

url = "https://api.agentpmt.com/products/purchase"

headers = {
    "Content-Type": "application/json",
    "Authorization": "Bearer ********"
}

data = {
    "product_id": "68b648923c0101597b3cd884",
    "parameters": {
        "action": "exponential",
        "source": "quantum",
        "count": 1,
        "rate": 1
    }
}

response = requests.post(url, headers=headers, json=data)
print(response.status_code)
print(response.json())

const url = "https://api.agentpmt.com/products/purchase";

const headers = {
  "Content-Type": "application/json",
  "Authorization": "Bearer ********"
};

const data = {
  product_id: "68b648923c0101597b3cd884",
  parameters: {
    "action": "exponential",
    "source": "quantum",
    "count": 1,
    "rate": 1
  }
};

fetch(url, {
  method: "POST",
  headers,
  body: JSON.stringify(data)
})
  .then(response => response.json())
  .then(data => console.log(data))
  .catch(error => console.error("Error:", error));

const axios = require('axios');

const url = "https://api.agentpmt.com/products/purchase";

const headers = {
  "Content-Type": "application/json",
  "Authorization": "Bearer ********"
};

const data = {
  product_id: "68b648923c0101597b3cd884",
  parameters: {
    "action": "exponential",
    "source": "quantum",
    "count": 1,
    "rate": 1
  }
};

axios.post(url, data, { headers })
  .then(response => {
    console.log(response.status);
    console.log(response.data);
  })
  .catch(error => {
    console.error("Error:", error.message);
  });

Login to view your API and budget keys. The example above uses placeholder values. Sign in to see personalized code with your bearer token.

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.

Recommended

Credit-Based Access Using AgentAddress

AgentAddress is preferred when an autonomous agent needs persistent file access, stored platform state, or maximum tool use ability across repeated calls.

Open Credit-Based Access Using AgentAddress

Direct x402 Payment

Use direct x402 for independent one-off tool calls that do not require shared files or stored platform state.

Accepted public payments

Stablecoin: USDC
Chains: Base, Arbitrum, Optimism, Polygon, and Avalanche

Direct x402 payments are not enabled for this product; use AgentAddress credit access instead.

Product Skill Package

This product has a published Agent Skill package. Install it when an autonomous agent needs product-specific operating instructions in its local skill registry.

Download SKILL.md View package source OpenClaw listing

OpenClaw install

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skills.sh install

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Usage Instructions

Usage guidance provided directly by the developer for this product.

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
}

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
}

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
}

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
}

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
}

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?

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

Install commands

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:

Hosted MCP config

{
  "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 for more details.

How does an external agent use this tool?

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

Agent prompt

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.

Quantum Distribution Generator

Available ActionsEach successful request consumes credits as outlined below.

Details

Use Cases

Dynamic MCP Setup

30 Second Setup

Hosted Streamable HTTPS

Config Example

Frequently Asked Questions

How do I connect this tool to an external agent?

How does an external agent use this tool?

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