--- name: risk-distribution-fitter-dbd3987480c5 description: Probability distribution fitting skill for calibrating uncertainty models from historical data or expert judgment allowed-tools: - Read - Write - Glob - Grep - Bash metadata: specialization: decision-intelligence domain: business category: simulation priority: medium tools-libraries: - scipy.stats - fitter - pomegranate - distfit graph: domains: [domain:business-intelligence] skillAreas: [skill-area:quantitative-modeling, skill-area:statistical-analysis, skill-area:financial-risk-modeling] roles: [role:quantitative-analyst, role:risk-analyst, role:data-scientist] --- # Risk Distribution Fitter ## Overview The Risk Distribution Fitter skill provides capabilities for calibrating probability distributions from historical data or expert judgment. It supports both data-driven fitting using statistical methods and expert elicitation protocols for subjective probability assessment. ## Capabilities - Maximum likelihood estimation (MLE) - Method of moments estimation - Bayesian parameter estimation - Goodness-of-fit testing (KS, AD, Chi-square) - Distribution comparison and selection - Expert elicitation protocol support (3-point, 5-point) - PERT distribution calculation - Visualization of fitted distributions ## Used By Processes - Monte Carlo Simulation for Decision Support - Predictive Analytics Implementation - Decision Quality Assessment ## Usage ### Data-Driven Fitting ```python # Fit distributions to historical data fitting_config = { "data": [/* historical observations */], "candidate_distributions": [ "normal", "lognormal", "gamma", "weibull", "exponential", "beta", "triangular" ], "fitting_method": "mle", "selection_criterion": "AIC" } ``` ### Expert Elicitation ```python # 3-point estimate (PERT) expert_estimate = { "method": "PERT", "minimum": 50000, "most_likely": 75000, "maximum": 120000, "confidence_level": 0.90 # optional: confidence that true value is within range } # 5-point estimate (for more precision) detailed_estimate = { "method": "5_point", "P10": 45000, "P25": 60000, "P50": 75000, "P75": 95000, "P90": 115000 } ``` ### Supported Distributions | Distribution | Use Case | Parameters | |-------------|----------|------------| | Normal | Symmetric, unbounded | mean, std | | Lognormal | Right-skewed, positive | mu, sigma | | Triangular | Bounded with mode | min, mode, max | | PERT | Bounded, weighted mode | min, mode, max | | Uniform | Equal probability | min, max | | Beta | Bounded, flexible shape | alpha, beta | | Gamma | Positive, right-skewed | shape, scale | | Weibull | Reliability/time | shape, scale | | Exponential | Memoryless | rate | ### Goodness-of-Fit Tests - **Kolmogorov-Smirnov (KS)**: Distribution-free, sensitive to center - **Anderson-Darling (AD)**: More sensitive to tails - **Chi-Square**: Categorical/binned data - **Cramér-von Mises**: Similar to KS, different weighting ### Model Selection Criteria - **AIC (Akaike Information Criterion)**: Balance fit and complexity - **BIC (Bayesian Information Criterion)**: Stronger penalty for parameters - **Log-Likelihood**: Raw fit quality ## Input Schema ```json { "fitting_mode": "data_driven|expert_elicitation", "data_driven_config": { "data": ["number"], "candidate_distributions": ["string"], "fitting_method": "mle|mom|bayesian", "selection_criterion": "AIC|BIC|likelihood" }, "expert_elicitation_config": { "method": "3_point|5_point|PERT|direct", "estimates": "object", "confidence_level": "number" }, "options": { "gof_tests": ["KS", "AD", "chi_square"], "visualize": "boolean", "compare_all": "boolean" } } ``` ## Output Schema ```json { "best_fit": { "distribution": "string", "parameters": "object", "gof_statistics": { "test_name": { "statistic": "number", "p_value": "number" } }, "selection_score": "number" }, "all_fits": [ { "distribution": "string", "parameters": "object", "scores": "object" } ], "summary": { "mean": "number", "std": "number", "percentiles": "object" }, "visualization_path": "string", "recommendations": ["string"] } ``` ## Best Practices 1. Use data-driven fitting when sufficient historical data exists (n > 30) 2. Validate fitted distributions against holdout data 3. Use PERT for expert estimates when asymmetry is expected 4. Document expert credentials and elicitation process 5. Consider mixture distributions for multimodal data 6. Always visualize fitted distribution against data/estimates 7. Use multiple goodness-of-fit tests for robustness ## Expert Elicitation Guidelines 1. Explain probability concepts clearly 2. Use familiar reference points 3. Ask for extreme estimates first, then middle 4. Check for overconfidence (typical: too narrow ranges) 5. Consider debiasing techniques 6. Document reasoning behind estimates ## Integration Points - Feeds into Monte Carlo Engine for simulation inputs - Supports Calibration Trainer for expert accuracy assessment - Connects with Bayesian Network Analyzer for CPT estimation - Integrates with Risk Register Manager for risk quantification --- Source attribution: a5c-ai Original project: https://github.com/a5c-ai/babysitter License: MIT License information: https://opensource.org/license/mit Original upstream instructions; downloaded from Mega AI Hub. ## Upstream license notice MIT License Copyright (c) 2026 Gabriel Moreira Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. # Mega AI Hub resource metadata Creator / publisher: a5c-ai Original project: https://github.com/a5c-ai/babysitter Attribution basis: Upstream repository explicitly recorded in package mirror path Fields of work: Data & Analytics, Marketing, Product Management, Sales Roles: Business Development, Data Analyst, Growth Marketer, Marketing Analyst, Product Manager Specialties: API Tools: Distfit, Fitter, Pomegranate, Scipy.Stats Country applicability: Country not specified Classification basis: Source catalog labels Instruction SHA-256: 1b3e52593d5b4fcc8fd993ace9a9ffbe5f7c44f1e51081b78a2cc049ce022160