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.
- Common use cases: non-negative values, scores bounded to [0,100], probability-like values in [0,1], and rare-event tail sampling.
- Truncation changes the mean/variance and can create mass near boundaries — check the PDF/CDF and sample stats.
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.
Do not use this tool as the sole basis for high-stakes decisions (medical/financial/legal). You don’t need to enter personal information to use it.
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)
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.
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