THE FEUTEX TOOLKIT

Gamma Distribution Moments

Inspect a gamma distribution’s mean, variance, skewness and excess kurtosis using shape and scale.

Probability workspace● Runs in your browser

01 Your input

ShapenumberScalevalue

02 Your result

View or copy raw result data

Result data

FormulaMean = shape*scale; Variance = shape*scale**2; Skewness = 2/sqrt(shape); Excess Kurtosis = 6/shape

Sources and model references

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

Worked example

Inputs

Shape: 4 number
Scale: 2 value

Expected results

Mean: 8 number
Variance: 16 number
Skewness: 1 number
Excess Kurtosis: 1.5 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

{
  "shape": 4,
  "scale": 2
}

Accuracy and scope

Uses scale, not rate; does not evaluate incomplete gamma probabilities. 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.