When is the log-normal distribution appropriate? Iv'e read the Wikipedia entry about the log-normal distribution, as well as a few other sources online, and still do not understand what sort of natural processes are expected to produce a log-normal distribution.
I understand how this distribution arises in processes with many independent factors whose effect is multiplicative, but not which processes are expected to behave in this way.
Both the Wikipedia entry and this review supply several examples of log-normally distributed phenomena, but the only one (aside from the multiplicative Galton board) for which I understand why the effect is multiplicative, is the distribution of bacteria colony sizes - The colonies double in number at each successive division, and the log of the colony size, the number of divisions, should be normally distributed.
Question:
Could anyone explain why the many examples of log-normally distributed data are multiplicative in nature, and more generally, how one comes to suspect , a-priori, such multiplicative phenomena as opposed to additive?
 A: I can give one example where one might suspect multiplicative effects, leading to a lognormal distribution.
Retailers like supermarkets have to forecast their demand (Fildes et al, 2018). Demand is influenced by many factors, like seasonality (intra-weekly and intra-yearly), calendar events, promotions and prices.
A promotion on ice cream will have a much higher additive uplift in summer than in winter. The effect will also be higher on Saturday than on Wednesday (Saturdays are usually much higher selling days than Wednesdays, at least in Europe and the US).
This motivates multiplicative models. Yes, sales are usually count data, so a continuous distribution is not really appropriate, but especially on aggregate data, the approximation is often good enough.
And as a matter of fact, sales forecasting in retail often does use models on logged data. A random example would be autoregressive distributed lags (ADL) models as, e.g., in Huang, Fildes & Soopramanien (2014):

(Sorry for just posting a screenshot, but this is for illustration only, anyway.)
