Hello Noëla Remond-Derbez ,

What lognorm.dist does in excel is force the values, no matter what the shape of a distribution of values (x) so that that [ln(x) - mu(x)] / sd(x) has a normal distribution. That's akin to taking percentile points of some arbitrary distribution and replacing them with z scores (e.g, 84th percentile = +1.0 z) under the assumption that the distribution genuinely has the symmetric, unimodal shape associated with the standard normal distribution.

Is that suitable? Only if you can argue that you knew the underlying distribution to be (log)normal in the first place, and that any departure from that was simply sampling variation. Otherwise, you have applied a non-reversible transform (unlike, say, a square root which can be reversed by squaring the transformed values) that forces the issue.

There are many data sets which will never transform with a reversible process to a normal distribution. That's just one of the joys of working with real world data. In such instances, the best tactic might be to seek an analytic method that does not require normality. As well, remember that, for most statistical methods which do require assumptions of normality, this applies to the model errors (estimated by residuals from the fitted model).

Good luck with your work.

Hello David Morse ,

Thank you very much for taking the time to share your knowledge, your answer is really rich and constructive.

All the best,

The distribution is occasionally referred to as the Galton distribution or Galton's distribution, after Francis Galton. The log-normal distribution has also been associated with other names, such as McAlister, Gibrat and Cobb–Douglas.[3]

A log-normal process is the statistical realization of the multiplicative product of many independent random variables, each of which is positive. This is justified by considering the central limit theorem in the log domain (sometimes called Gibrat's law). The log-normal distribution is the maximum entropy probability distribution for a random variate X—for which the mean and variance of ln(X) are specified.