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.

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

Connect Your Agent In 5 Min

Use hosted MCP first, or install the local STDIO fallback when your client requires a command

Hosted Streamable HTTPS

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

Endpoint: https://api.agentpmt.com/mcp
Authorization: Bearer <AGENTPMT_BEARER_TOKEN>

Full connection guide

Local STDIO Fallback

Use the local router for Claude Code, Codex, Cursor, Zed, and other clients that require a command-based MCP server. The router forwards requests to the hosted endpoint and does not execute tools locally.

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

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.

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

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.

Quantum Distribution Generator

Available ActionsEach successful request consumes credits as outlined below.

Details

Use Cases

Actions(7)

Connect Your Agent In 5 Min

Hosted Streamable HTTPS

Local STDIO Fallback

Credit-Based Access Using AgentAddress

Direct x402 Payment

Usage Instructions

Quantum Distribution Generator

Actions

exponential

poisson

binomial

beta

gamma

montecarlo_sample

randomwalk

Common Workflows

Risk Simulation

A/B Test Modeling

Stock Price Path Simulation

Bayesian Parameter Estimation

Important Notes

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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