Home / Statistical Tools / Distribution Fit/Calc / Distribution Fit / Gumbel Distribution
Gumbel Distribution¶
Distribution Fitting: Non-Reliability¶
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QXL Stat Tools Tab > Distribution Fit/Calc > Distribution Fit > 2-Param Gumbel
Distribution Fitting: Reliability¶
Uncensored Data
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QXL Stat Tools Tab > Reliability > Uncensored > 2-Param Gumbel
Probability Calculator¶
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QXL Stat Tools Tab > Distribution Fit/Calc > Distribution Calculator > Gumbel
The Gumbel distribution is a continuous probability distribution. Quantum XL uses the smallest extreme value (SEV) form of the Gumbel distribution, one of the family of extreme value distributions, commonly used in reliability to model the minimum of a set of values. The equation for the probability density function (pdf) is below.
| Parameters | \(-\infty < \mu < +\infty \qquad \mu = Location\) \(\sigma > 0 \qquad \sigma = Scale\) |
| Support | \(x \in (-\infty, +\infty)\) |
| Probability density function (pdf) | \(f(x) = \dfrac{1}{\sigma} e^{\left(z - e^{z}\right)}\) where \(z = \frac{(x - \mu)}{\sigma}\) |