Basic Concepts
From Lognormal Distribution, we know that
Thus
and so
from which it follows that
and so
or
Since
it follows that
and so
which gives us the estimates for μ and σ based on the method of moments.
Example
Example 1: Estimate the mu and sigma parameters for the log-normal distribution that fits the sample of size 100 in column A of Figure 1 (only the first 8 elements are displayed) using the method of moments.
Figure 1 – Fitting a lognormal distribution
The formula for the log-likelihood function (cell D9) is
=-D2*(LN(2*PI())/2+LN(D4)+(D3/D4)^2/2)+(D3/D4^2-1)*SUM(LN(A2:A101))-SUMSQ(LN(A2:A101))/(2*D4^2)
This formula is derived in Fitting Lognormal Parameters via MLE.
Examples Workbook
Click here to download the Excel workbook with the examples described on this webpage.
Reference
Genos, B. F. (2009) Parameter estimation for the Lognormal distribution
https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=2927&context=etd