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THE FEUTEX TOOLKIT

Gumbel Maximum Distribution

Evaluate a Gumbel maximum distribution’s cumulative probability, median and variance.

Probability workspace● Runs in your browser
01 Your input
02 Your result
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FormulaCdf = exp(-exp(-(x-mu)/b)); Median = mu-b*log(log(2)); Variance = PI**2*b**2/6
Sources and model references

Worked example

Inputs

Location
0 value
Scale
2 value
Evaluation value
0 value

Expected results

Cdf
0.3678794412 probability
Median
0.7330258412 number
Variance
6.579736267 number

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter the labeled inputs using consistent units.
  2. Check the stated assumptions and calculate.
  3. Review each output and compare another input scenario.

Try this example

{
  "mu": 0,
  "b": 2,
  "x": 0
}

Accuracy and scope

Maximum-type convention F(x)=exp(−exp(−(x−μ)/β)); minimum-type conventions differ. Finite floating-point arithmetic; results can lose precision near singular or extreme inputs.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.