Distribution Analysis
Analyze and fit statistical distributions: normality tests, distribution fitting, skewness and kurtosis interpretation, QQ plots, and distribution comparison. Use when assessing data normality, choosing statistical tests, or understanding data generating processes.
Install
$ agentstack add skill-ericwang915-data-scientist-skills-distribution-analysis ✓ scanned · ✓ verified, works with Claude Code, Cursor, and more.
Security review
✓ PassedNo issues found. Passed automated security review. · v0.1.0 How review works →
- ✓ Prompt-injection patterns
- ✓ Secret / credential exfiltration
- ✓ Dangerous shell & filesystem operations
- ✓ Untrusted network calls
- ✓ Known-malicious package signatures
What it can access
- ✓ Network access No
- ✓ Filesystem access No
- ✓ Shell / process execution No
- ✓ Environment & secrets No
- ✓ Dynamic code execution No
From automated source analysis of v0.1.0. “Used” means the capability is present in the source — more access means more to trust, not that it’s unsafe.
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Declared compatibility
Compatibility is declared by the source manifest. End-to-end runtime verification is coming, see below.
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Distribution Analysis
Purpose
Characterize the statistical distribution of your data. Determines whether data is normal, identifies the best-fitting distribution, and provides the right statistical tools based on the distribution shape.
How It Works
Step 1: Visual Assessment
- Histogram with KDE overlay
- QQ plot against normal distribution
- Box plot with outlier markers
- ECDF (Empirical Cumulative Distribution Function)
Step 2: Normality Testing
- Shapiro-Wilk test (best for n < 5000)
- D'Agostino-Pearson test (combines skewness and kurtosis)
- Anderson-Darling test (sensitive to tails)
- Kolmogorov-Smirnov test (general goodness-of-fit)
Step 3: Distribution Fitting
Fit candidate distributions and rank by goodness-of-fit:
- Normal, Log-normal, Exponential, Gamma, Beta, Weibull, Poisson, Uniform
- AIC/BIC comparison across candidates
- Best-fit parameters with confidence intervals
Step 4: Transformation Recommendations
If non-normal:
- Log transform (right-skewed data)
- Box-Cox transform (optimal power transform)
- Yeo-Johnson transform (handles negative values)
- Square root transform (count data)
Step 5: Practical Implications
- Which statistical tests are appropriate (parametric vs. non-parametric)
- Impact on confidence intervals and hypothesis tests
- Modeling recommendations (GLM family choice, kernel selection)
Usage Examples
"Is this revenue data normally distributed? What transformation should I apply?""Fit the best distribution to this event time data for simulation modeling"Output Format
- Visual Summary: Histogram, QQ plot, box plot
- Test Results: Normality test p-values with interpretation
- Best Fit: Distribution name, parameters, goodness-of-fit metrics
- Transformation: Recommended transform with before/after comparison
- Python Code: Reproducible analysis script
Source & license
This open-source skill is cataloged on AgentStack and links to its original source — we do not rehost the code.
- Author: ericwang915
- Source: ericwang915/data-scientist-skills
- License: MIT
Install and usage instructions live in the source repository linked above.
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Versions
- v0.1.0 Imported from the upstream source.