Monte Carlo Engine

Usage

Distribution Specification

# Define input distributions
input_variables = {
    "revenue": {
        "distribution": "triangular",
        "parameters": {"min": 800000, "mode": 1000000, "max": 1500000}
    },
    "cost": {
        "distribution": "normal",
        "parameters": {"mean": 600000, "std": 50000}
    },
    "market_share": {
        "distribution": "PERT",
        "parameters": {"min": 0.05, "mode": 0.10, "max": 0.20}
    },
    "unit_price": {
        "distribution": "uniform",
        "parameters": {"min": 45, "max": 55}
    }
}

Correlation Matrix

# Define correlations between variables
correlations = {
    "variables": ["revenue", "cost", "market_share"],
    "matrix": [
        [1.0, 0.6, 0.3],   # revenue correlations
        [0.6, 1.0, 0.2],   # cost correlations
        [0.3, 0.2, 1.0]    # market_share correlations
    ]
}

Model Function

# Define the model to simulate
def profit_model(inputs):
    revenue = inputs["revenue"]
    cost = inputs["cost"]
    profit = revenue - cost
    return {"profit": profit, "margin": profit / revenue}

Sampling Strategies

1. Simple Random Sampling: Standard Monte Carlo
2. Latin Hypercube Sampling: Better coverage with fewer samples
3. Quasi-Monte Carlo: Low-discrepancy sequences (Sobol, Halton)
4. Importance Sampling: Focus on tail events

Convergence Monitoring

The skill monitors:

• Running mean and standard deviation
• Coefficient of variation convergence
• Percentile stability
• Adaptive stopping criteria

Input Schema

{
  "input_variables": {
    "variable_name": {
      "distribution": "string",
      "parameters": "object"
    }
  },
  "correlations": {
    "variables": ["string"],
    "matrix": "2D array"
  },
  "model": "function or expression",
  "simulation_options": {
    "iterations": "number",
    "sampling_method": "random|lhs|quasi_mc",
    "random_seed": "number",
    "parallel": "boolean",
    "convergence_threshold": "number"
  },
  "output_options": {
    "percentiles": ["number"],
    "risk_metrics": ["VaR", "CVaR"],
    "confidence_level": "number"
  }
}

Output Schema

{
  "summary_statistics": {
    "output_variable": {
      "mean": "number",
      "std": "number",
      "median": "number",
      "min": "number",
      "max": "number",
      "percentiles": "object"
    }
  },
  "risk_metrics": {
    "VaR": "number",
    "CVaR": "number",
    "probability_of_loss": "number"
  },
  "convergence_info": {
    "iterations_run": "number",
    "converged": "boolean",
    "stability_scores": "object"
  },
  "raw_results": "array (optional)",
  "tornado_data": "object",
  "visualization_paths": ["string"]
}

Best Practices

1. Use at least 10,000 iterations for stable percentile estimates
2. Apply Latin Hypercube Sampling for efficiency
3. Validate input distributions with subject matter experts
4. Include correlations for realistic results
5. Monitor convergence before accepting results
6. Perform sensitivity analysis to identify key drivers
7. Document all distribution assumptions

Integration Points

• Receives distributions from Risk Distribution Fitter
• Feeds into Sensitivity Analyzer for importance analysis
• Supports Value at Risk Calculator for risk metrics
• Connects with Decision Tree Builder for decision node valuation
• Integrates with Real Options Analyzer for option valuation