I need help with this basic question. A study found that a variable is log-normal, with mean A and percentiles p1, p2 and p3 (could be 10%, 50% and 90%).
Another study for a different group found that the mean is B, but provides no data on percentiles. I want to assume the two distributions are the same, except for scaling the mean. So, if I want to know the percentiles p1, p2 and p3 of this new distribution, is it just the scaling of p1 p2 and p3 by B/A?
For the log-normal, the mean is
and the quartile (which gives the percentiles ...?) is
$exp(u + s*sqrt(2)*erfinv(2F-1)$
If I scale the mean by a given factor, it seems from the above that it is not enough to scale the quartile by the same factor. Then, how can I do it?
Thank you for the help.