What is a Beta distribution?
The Beta distribution is a continuous distribution over (0,1). It’s commonly used for probabilities, rates, and proportions.
- α=β=1: uniform.
- α<1 and β<1: U-shaped (mass near 0 and 1).
- α>β: skewed toward 1. α<β: skewed toward 0.
- Large α and β: concentrated around the mean.
PDF: f(x)=x^(α-1)(1-x)^(β-1)/B(α,β). Mean: α/(α+β). Variance: αβ/[(α+β)^2(α+β+1)].
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Presets
Quickly set common shapes (you can tweak values after applying).
Generator
Set α/β, sample size, bins, and RNG. Then generate samples and export results.
Sample stats
Samples (first 20)
FAQ
What do α and β mean?
They control the shape of Beta(α,β). Larger α pushes mass toward 1; larger β pushes mass toward 0.
Why does it concentrate near 0 or 1?
If α<1 or β<1, the PDF can spike near 0 or 1. The chart clips the endpoints for stable drawing.
Is seeded RNG secure?
No. Seeded mode is for reproducibility only. Use Secure (CSPRNG) for security-sensitive randomness.
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