Multiplic

• $\mathrm{logMean}$: mean of log values (location parameter; $e^\mathrm{logMean}$ equals the geometric mean)
• $\mathrm{logStdDev}$: standard deviation of log values (scale parameter; controls multiplicative spread)

• Formation: the product of many positive variables $X_1 \cdot X_2 \cdot \ldots \cdot X_n$ with mild conditions (e.g., finite variance of $\log X$).
• Origin: historically called Log-Normal or Galton distribution after Francis Galton.
• Rename Motivation: renamed to $\underline{\operatorname{Multiplic}}$ to reflect its formation mechanism through multiplication.
• Properties: logarithm of a $\underline{\operatorname{Multiplic}}$ (LogNormal) variable follows an $\underline{\operatorname{Additive}}$ (Normal) distribution.
• Applications: stock prices, file sizes, reaction times, income distributions, biological growth rates.
• Caution: no perfectly multiplic distributions exist in real data; all real-world measurements contain deviations. Traditional estimators struggle with the inherent skewness and heavy right tail.