Search Ctrl K
Home / Tools
THE FEUTEX TOOLKIT

Lognormal Moment Profile

Find a lognormal model’s median, mean, variance and mode from natural-log parameters.

Probability workspace● Runs in your browser
01 Your input
02 Your result
View or copy raw result data
FormulaMedian = exp(mu); Mean = exp(mu+sigma**2/2); Variance = expm1(sigma**2)*exp(2*mu+sigma**2); Mode = exp(mu-sigma**2)
Sources and model references

Worked example

Inputs

Mean of natural log
0 log value
SD of natural log
0.5 log value

Expected results

Median
1 number
Mean
1.133148453 number
Variance
0.364695854 number
Mode
0.7788007831 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,
  "sigma": 0.5
}

Accuracy and scope

Parameters describe ln(X), not X. Extreme parameters may overflow. 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.