# genpark-hypothesis-welch-t-test-statistical-evaluator-skill

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[![Python 3.9+](https://img.shields.io/badge/python-3.9%2B-blue.svg?style=for-the-badge&logo=python)](https://www.python.org/)
[![License MIT](https://img.shields.io/badge/license-MIT-green.svg?style=for-the-badge)](LICENSE)
[![MCP Compatible](https://img.shields.io/badge/MCP-100%25%20Compatible-purple.svg?style=for-the-badge&logo=anthropic)](https://genpark.ai/mcp)
[![GenPark AI](https://img.shields.io/badge/Verified%20By-GenPark%20AI-orange.svg?style=for-the-badge&logo=openai)](https://genpark.ai)
[![Zero Dependencies](https://img.shields.io/badge/Dependencies-0%20(Stdlib%20Only)-brightgreen.svg?style=for-the-badge)](requirements.txt)

<p align="center">
  <b>Production-Grade Data Science & Statistical Agent Skill</b> • <b>100% Standard Library Python</b> • <b>Native Model Context Protocol (MCP)</b>
</p>

</div>

---

## ⚡ Overview & Architectural Significance

`genpark-hypothesis-welch-t-test-statistical-evaluator-skill` delivers zero-dependency, mathematically rigorous statistical modeling, time-series forecasting, and anomaly detection primitives engineered strictly using Python 3.9+ standard library.

### 🌟 Key Architectural Capabilities
- **Zero External Dependencies**: Operates exclusively via pure Python (`math`, `random`, `statistics`, `json`). Zero pip install overhead, zero numpy/scipy compilation failures.
- **Enterprise Statistical Invariants**: Implements formal Holt linear smoothing, modified Z-score & Tukey IQR anomaly bounds, Welch's t-test p-value estimations, multivariate linear regression via gradient descent, and Power Iteration PCA dimensionality reduction.
- **Native Anthropic MCP Protocol**: Compliant with standard JSON-RPC 2.0 stdio MCP specifications for Claude Desktop, Cursor, and Windsurf.

---

## 🏗️ Architectural Topology & State Machine

```mermaid
flowchart TD
    DataStream["Time-Series & Multidimensional Numerical Stream"] --> AnomalyDetector["Statistical Z-Score & IQR Anomaly Detector"]
    
    AnomalyDetector -->|Outlier Detected| FlagAnomaly["Flag Outlier & Alert Telemetry"]
    AnomalyDetector -->|Clean Stream| ModelingBranch{"Analytical Objective"}
    
    ModelingBranch -->|Trend Forecasting| HoltForecaster["Holt Linear Exponential Smoothing Forecaster"]
    ModelingBranch -->|Supervised Fitting| LinearRegression["Multivariate Gradient Descent Regression Engine"]
    ModelingBranch -->|Hypothesis Testing| WelchTest["Welch's Two-Sample T-Test Evaluator"]
    ModelingBranch -->|Dimensionality Reduction| PCAReducer["Power Iteration SVD/PCA Dimension Reducer"]
    
    HoltForecaster --> Synthesis["Agent Synthesis & Statistical Report"]
    LinearRegression --> Synthesis
    WelchTest --> Synthesis
    PCAReducer --> Synthesis
```

---

## 🚀 Quickstart & Standalone Execution

### Local Python Client Usage

```python
from client import HypothesisWelchTTestEvaluator

# Initialize engine
engine = HypothesisWelchTTestEvaluator()

# Execute self-testing benchmark suite
result = engine.run_benchmark_welch_t_test()
print("Execution Result:", result)
```

---

## 🔌 One-Click MCP Integration (Claude Desktop / Cursor)

Add to your `claude_desktop_config.json` or `cursor.json`:

```json
{
  "mcpServers": {
    "genpark-hypothesis-welch-t-test-statistical-evaluator-skill": {
      "command": "python",
      "args": ["-u", "/path/to/genpark-hypothesis-welch-t-test-statistical-evaluator-skill/mcp_server.py"]
    }
  }
}
```

---

## 📦 Smithery.ai & PyPI Deployment

This skill contains pre-configured `smithery.yaml` and `pyproject.toml` manifests. Install directly via pip:

```bash
pip install git+https://github.com/alphaparkinc/genpark-hypothesis-welch-t-test-statistical-evaluator-skill.git
```

---

<div align="center">
  <sub>Maintained with ❤️ by <b><a href="https://genpark.ai">GenPark AI Engineering</a></b> • Powering Next-Gen Autonomous Data Agents 🌍</sub>
</div>