What is a Weibull distribution?
The Weibull distribution is a standard model for lifetimes, failure times, and waiting times (x≥0).
- k=1: exponential-like.
- k<1: more mass near 0 (often “decreasing hazard”).
- k>1: a peak appears (often “increasing hazard”).
- λ scales the overall time/length (bigger λ → larger values).
PDF: f(x)=(k/λ)(x/λ)^(k-1)exp(-(x/λ)^k). Mean: λ·Γ(1+1/k). Variance: λ²(Γ(1+2/k)-Γ(1+1/k)²). Median: λ·(ln 2)^(1/k).
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Presets
Quickly set common shapes (you can tweak values after applying).
Generator
Set k/λ, sample size, bins, and RNG. Then generate samples and export results.
Sample stats
Samples (first 20)
FAQ
What do k and λ mean?
k is shape and λ is scale. k changes the curve shape; λ scales the overall magnitude.
Why does it concentrate near 0 when k<1?
For k<1, the density can spike near 0. The PDF drawing avoids exact 0 for stability.
Is seeded RNG secure?
No. Seeded mode is for reproducibility only. Use Secure (CSPRNG) for security-sensitive randomness.
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