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Truncated Normal Generator & Visualizer

Generate bounded normal (truncated Gaussian) samples with lower/upper limits, then visualize histogram + PDF/CDF.

Everything runs in your browser; nothing is uploaded. Share URLs contain settings only (no generated samples).

Secure mode uses CSPRNG. Seeded mode is for reproducibility, not secrecy.

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What is a truncated normal?

A truncated normal is a normal distribution conditioned to stay within bounds such as a≤X≤b. It is also known as a bounded normal or truncated Gaussian.

How it works: it uses the inverse CDF method (sample a uniform random number and map it through the truncated CDF). This avoids rejection-sampling slowdowns when truncation is extreme.

Use this tool as a learning reference for high-stakes domains (medical/financial/legal), and verify final decisions with qualified sources. You don’t need to enter personal information.

Presets

Pick a practical preset (you can tweak values after applying). It regenerates instantly.

Tip: presets are meant as starting points.

Generator

Set μ/σ and bounds, then generate samples and export results.

Sample stats

Samples (first 20)


      

    

  


  
How to use this tool effectively
This guide helps you use Truncated Normal Generator & Visualizer in a repeatable way: define a baseline, change one variable at a time, and interpret outputs with explicit assumptions before you share or act on results.
How it works
The page applies deterministic logic to your inputs and shows rounded output for readability. Treat it as a comparison workflow: run one baseline case, adjust a single parameter, and measure both absolute and percentage deltas. If a result seems off, verify units, time basis, and sign conventions before drawing conclusions. This approach keeps your analysis reproducible across teammates and sessions.
When to use
Use this page when you need a fast estimate, a classroom check, or a practical what-if comparison. It works best for planning and prioritization steps where you need direction and magnitude quickly before investing in deeper modeling, manual spreadsheets, or formal external review.
Common mistakes to avoid
Interpretation and worked example
Run a baseline scenario and keep that result visible. Next, modify one assumption to reflect your realistic alternative and compare direction plus size of change. If the direction matches your domain expectation and the size is plausible, your setup is usually coherent. If not, check hidden defaults, boundary conditions, and interpretation notes before deciding which scenario to adopt.
See also

    
FAQ

    
What is a truncated normal?
A normal distribution conditioned to stay inside bounds. This tool supports two-sided and one-sided truncation.

    
Why does the mean shift?
Truncation removes probability mass outside the bounds. The remaining mass is renormalized, so mean/variance change.

    
What does Z mean?
Z=Φ(β)−Φ(α) is the probability the original normal lands inside the bounds. Smaller Z means “more extreme” truncation.

    
Is seeded RNG secure?
No. Seeded mode is for reproducibility only. Use Secure (CSPRNG) for security-sensitive randomness.

  
What should I do first on this page?
Start with the minimum required inputs or the first action shown near the primary button. Keep optional settings at defaults for a baseline run, then change one setting at a time so you can explain what caused each output change.


  
How to use Truncated Normal Generator & Visualizer effectively
How this tool helps
Tools are designed for quick scenario comparisons. They work best when you keep one question per run, define success criteria first, and avoid switching objectives mid-stream. This reduces decision noise and produces results you can defend in follow-up review.
Input validation checklist
Before running, verify that required values are in the right format, that optional flags are intentionally set, and that baseline assumptions reflect current conditions. Invalid assumptions are often mistaken for tool bugs, so validation is part of interpretation quality.
Scenario planning pattern
Build three rows: conservative, expected, and aggressive cases. Keep data sources transparent for each case and compare output spacing. The pattern helps you spot non-linear jumps and decide whether a model is stable under plausible variation.
When to revisit inputs
Revisit inputs when input scale changes, time window shifts, or downstream decisions add new constraints. If constraints change, your previous output remains a useful reference but should not be treated as final guidance.
Operational checkpoint 1
Record the exact values and intent before you finalize any comparison. Confirm the unit system, date context, and business constraints. Compare outputs side by side and check whether differences are explained by one changed variable or by hidden assumptions. This checkpoint often reveals the single factor that changed everything.
Operational checkpoint 2
Record the exact values and intent before you finalize any comparison. Confirm the unit system, date context, and business constraints. Compare outputs side by side and check whether differences are explained by one changed variable or by hidden assumptions. This checkpoint often reveals the single factor that changed everything.