THE FEUTEX TOOLKIT

Pareto Tail Profile

Calculate Pareto exceedance probability and finite moments for a heavy-tailed model.

Probability workspace● Runs in your browser

01 Your input

Minimum supportvalueShapenumberThresholdvalue

02 Your result

View or copy raw result data

Result data

FormulaTail = (xm/x)**alpha; Mean = alpha*xm/(alpha-1); Variance = alpha*xm**2/((alpha-1)**2*(alpha-2))

Sources and model references

https://mathworld.wolfram.com/ParetoDistribution.html

Worked example

Inputs

Minimum support: 1 value
Shape: 3 number
Threshold: 2 value

Expected results

Tail: 0.125 probability
Mean: 1.5 number
Variance: 0.75 number

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

How to use this tool

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

Try this example

{
  "xm": 1,
  "alpha": 3,
  "x": 2
}

Accuracy and scope

Shape restricted above 2 so both mean and variance are finite. 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.