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Main question:
If I read in a paper that a particular dataset's best fit is lognormal with $\mu=7.7$ and $\sigma=1.9$, what is the location, scale, and shape parameter of the lognormal?

Side questions:
Is the scale parameter $e^\mu$ or $\sigma$? I see different statements in different reference literature.

Is $\mu$ given in the paper equal to the mean of the transformed normal or to some new transformed $\mu$?

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Naturally I can't speak authoritatively about any unreferenced papers you (don't) cite, but you appear to be encountering common conventions, apart from one mistake.

You are being given location and scale on the back-transformed (logged) scale; things are simplest on that scale as the equivalent normal has

  1. Mean, median and mode identical at $\mu$.

  2. A statistically natural scale parameter, namely the standard deviation of logged values $\sigma$.

  3. Simple shape properties, those of the normal.

When the distribution is exponentiated to become lognormal, mean, median and mode now differ. $e^\mu$ is the median, so cannot be regarded as a scale parameter. But the mean and mode and variance all depend on both $\mu$ and $\sigma$. Skewness and kurtosis depend on $\sigma$, so to the best of my knowledge there is no reason to seek or to quote a shape parameter, shape being determined by $\sigma$.

http://en.wikipedia.org/wiki/Lognormal is useful. (The entries on distributions in Wikipedia seem of higher quality than some of the other statistical content.)

(The usual terminology of lognormal is entrenched, but it is, I suggest, backwards. A lognormal is an exponentiated normal. Perhaps "expnormal" sounded too ugly, but I guess "lognormal" sounded ugly when introduced. It is also true, naturally, that a lognormal is defined by the fact that if you take logarithms, you get a normal, but it seems more fundamental to define a distribution by how it is generated, not by how you should want to transform it.)

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  • $\begingroup$ Is σ (as you mentioned, it probably refers to the logged standard deviation) the same as the corresponding Normal σ (i.e., if you back transform the lognormal to the normal, will you get the same σ?)? In other words, if I take μ=7.7 and σ=1.9 to generate normal variates and then exponentiate those variates, will I get similar data as the dataset that the paper references? $\endgroup$
    – Wuschelbeutel Kartoffelhuhn
    Commented Jul 31, 2013 at 18:21
  • $\begingroup$ Same comment: I don't know what paper you are referring to. Important detail: $\sigma$ is the standard deviation of the logged values, not the logged standard deviation, e.g. sd(ln(x)) not ln(sd(x)). otherwise yes, that sounds right. $\endgroup$
    – Nick Cox
    Commented Jul 31, 2013 at 18:26
  • $\begingroup$ Thanks for your answers. Footnote on page 13 gla.ac.uk/media/media_238147_en.pdf If you say that σ is the standard deviation of the logged values, it's not intuitive to me that σ is also the correct standard deviation of the underlying Normal (not Lognormal). $\endgroup$
    – Wuschelbeutel Kartoffelhuhn
    Commented Jul 31, 2013 at 19:42
  • $\begingroup$ If the authors' meaning is not clear to you, I suggest you contact them directly. My impression is that they are using the same convention as I have described, but I am not going to read the whole paper or do further work to check what they did. $\endgroup$
    – Nick Cox
    Commented Jul 31, 2013 at 21:23

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