Monte Carlo Analysis

Convert an unstructured risk question into a structured Monte Carlo run via the bundled scripts/monte_carlo.py toolkit. Sample from the right distribution, summarise percentiles, and return a histogram PNG plus spreadsheet export. Offer an interactive HTML chart when the user asks for it.

Instructions

1. Cognitive intake. Detect the core question (timeline, financial risk, yield, downtime, claims, etc.). If the user did not give enough numbers to parameterise a distribution, stop and ask — do not invent bounds. Prompt with the distribution options below.

2. Choose a distribution:

   • Triangular — user gives Minimum, Most Likely (peak), Maximum.
   • Normal — user gives Mean and Std Dev (optional base_modifier for portfolio / compounding style: outcome = base * (1 + return)).
   • Uniform — every value between Minimum and Maximum is equally likely.
   • Log-normal — non-negative, right-skewed risks; user gives log-scale mean and sigma. Highlight the Mean vs P50 gap when skew is large.
   • Poisson — count of rare events in a fixed interval; user gives lambda (expected count per interval, e.g. outages per month).
   • Weibull — time-to-failure / reliability; user gives shape (k) and scale (λ). Shape < 1 → infant mortality, = 1 → exponential, > 1 → wear-out.
   • Beta — bounded probability [0, 1] or percentage; user gives alpha and beta. Useful for proportions, conversion rates, or task-completion estimates.
   • Exponential — memoryless inter-arrival times; user gives scale (mean = 1 / rate). Good for time between random events (calls, failures, requests).

3. Defaults. If simulations are unspecified, use 10000. Prefer a clear chart_title and x_axis_label in the user's domain units (days, USD, hours).

4. Execute with the toolkit (import or CLI). Always produce:

   • Summary stats: mean, P5, P50, P95
   • PNG histogram with P5 / P50 / P95 marker lines
   • CSV of all iterations (opens in Excel)

   Also produce when asked:

   • Interactive HTML — self-contained Chart.js page with live sliders per distribution parameter, a simulations count slider, and a P-threshold calculator (P(outcome < X) = ?)
   • .xlsx workbook (requires openpyxl; otherwise point them to the CSV)

pythonCopy code
import sys
sys.path.insert(0, "scripts")
from monte_carlo import simulate

result = simulate({
    "distribution": "triangular",
    "low": 12, "peak": 18, "high": 45,
    "simulations": 10000,
    "chart_title": "Cloud migration duration (days)",
    "x_axis_label": "Days",
    "html": True,          # optional interactive Chart.js page with live controls
    "excel": True,         # optional .xlsx (falls back to CSV if openpyxl missing)
    "out_prefix": "simulation",
})
# result keys: mean, p5, p50, p95, brief_summary, chart_path, csv_path, …

5. Present results in domain language:

   • P5 = downside / late / risk baseline
   • P50 = median expectation
   • P95 = optimistic / upper ceiling (or severe upside for cost/risk)
   • Show or link the PNG; mention CSV/Excel paths; offer HTML if not requested yet.
   • Always end with a brief summary (2–3 sentences). Prefer result["brief_summary"] from the toolkit; you may lightly rephrase it into the user's domain (days, dollars, hours) without changing the numbers.

6. Response layout (adapt labels to the domain):

markdownCopy code
### Simulation Analytics Report
Ran {simulations} iterations ({distribution}).

| Metric | Value |
| --- | --- |
| P5 (risk baseline) | {p5} |
| P50 (median) | {p50} |
| P95 (upper) | {p95} |
| Mean | {mean} |

Histogram: {chart_path}
Raw iterations: {csv_path}

### Brief summary
{brief_summary}

Guardrails

• Never run the script when required parameters are missing — ask first.
• Do not fabricate distribution parameters or claim false precision.
• Prefer the bundled toolkit over hand-rolled NumPy each time, for consistent charts and exports.
• Keep LLM replies to the summary payload; do not dump all iteration rows into chat.

Bundled files

• scripts/monte_carlo.py — simulation engine, PNG, CSV/Excel, interactive HTML
• references/cheatsheet.md — parameters, CLI, test prompts
• assets/sample_triangular.json — demo payload (project timeline)
• assets/sample_normal.json — demo payload (portfolio returns)
• assets/sample_lognormal.json — demo payload (skewed downtime)
• assets/sample_poisson.json — demo payload (event count per interval)
• assets/sample_weibull.json — demo payload (component lifetime)
• assets/sample_exponential.json — demo payload (time between arrivals)