Home / Statistical Tools / Distribution Fit/Calc / Distribution Fit / Weibull Distribution
Weibull Distribution (2-Parameter and 3-Parameter)¶
Distribution Fitting: Non-Reliability¶
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QXL Stat Tools Tab > Distribution Fit/Calc > Distribution Fit > 2-Param Weibull
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QXL Stat Tools Tab > Distribution Fit/Calc > Distribution Fit > 3-Param Weibull
Distribution Fitting: Reliability¶
Uncensored Data
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QXL Stat Tools Tab > Reliability > Uncensored > 2-Param Weibull
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QXL Stat Tools Tab > Reliability > Uncensored > 3-Param Weibull
Censored Data
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QXL Stat Tools Tab > Reliability > Censored > 2-Param Weibull
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QXL Stat Tools Tab > Reliability > Censored > 3-Param Weibull
Probability Calculator¶
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QXL Stat Tools Tab > Distribution Fit/Calc > Distribution Calculator > Weibull
The Weibull distribution is a continuous probability distribution named for Waloddi Weibull. The distribution is commonly used in reliability modeling. The Weibull distribution can be 2-Parameter and 3-Parameter. The probability density function (pdf) for the 3-Parameter Weibull is below. When Gamma (threshold) is zero, the 3-Parameter and 2-Parameter are equivalent. When Beta=1 and Gamma=0, the Weibull distribution is equivalent to the exponential distribution.
| Parameters | \(\alpha > 0\) Alpha, Scale \(\beta > 0\) Beta, shape (when \(\beta = 1\), the Weibull is equivalent to the exponential) \(-\infty < \gamma < +\infty\) Gamma, Offset (threshold) |
| Support | \(x \in [\gamma, +\infty)\) |
| Optimization parameter | \(\gamma\) Gamma, Offset (threshold) |
| Probability density function (pdf) | \(f(x) = \dfrac{\beta (x - \gamma)^{(\beta - 1)}}{\alpha^{\beta}} \, e^{-\left(\frac{(x - \gamma)}{\alpha}\right)^{\beta}}\) |
Note
The 2-parameter Weibull is identical to the 3-parameter Weibull when Gamma (offset, threshold) is zero.