Is there any good short terminology for the two parameters of a lognormal distribution?
I have been using mean-log for $\mu$ and volatility for $\sigma$, where the lognormal variable $X$ has $\ln(X)$ distributed normally with mean $\mu$ and standard deviation $\sigma$.
Mean-log has the advantages of being short, clear, and parallel to the well-established meaning of "mean square". It may not be parallel to the word "lognormal", but I still find it preferable to the alternative:
- "log-mean" would suggest $\ln(E(X))$.
Volatility works well for one common use of the lognormal distribution, e.g. modeling relative stock prices in one year by a lognormal distribution with mean-log 8.5% and volatility 19.5%. But this does not work so well for lognormal models of StackExchange votes or storm sizes. On the other hand, I find this preferable to the convolutedness or awkwardness of the alternatives:
- "modeling relative stock prices in one year by a lognormal distribution whose log has mean 8.5% and standard deviation 19.5%"
- "standard deviation of the log of the variable of 19.5%"
- "s.d.-log of 19.5%"
- "shape of 19.5%" (would one ever say that a normal distribution had a shape of 19.5%?)
- "sigma of 19.5%"
Does any one have any better short terminology to suggest?