Fitting a distribution on Income data Why is the Pareto Distribution a better fit to the upper tail of Income data, and the Lognormal distribution a better fit to the lower tail? What happens if we fit the data the other way around?
My argument is that if we truncate the hump of the lognormal distribution it should perform nicely as a fit for the upper tail, and I cannot find a good reason to suggest that the Pareto distribution should not be used as a fit for the lower tail.
 A: I would have thought that what is most suitable must be empirically justified.
I am used to looking at income distributions something like this (from the UK), though strictly speaking this is only the bottom 92% of the distribution

A Pareto distribution really does not work for the lower part of this distribution, as it fails to fit those incomes between zero and the mode.  (Just to catch the unwary, there is also a non-zero number of individuals with zero reported income, almost visible as about $0.55$ million in the graph)  
Again in the upper tail the justification for using a particular distribution would need to be empirical.  
Different income distributions form different countries might need different models
A: Consider the log of income.
The assertion corresponds to the claim that for log-income the left side of the distribution is closer to normal but the right side has a tail that is more like an exponential. If it's the case in a particular data set, this should be able to be seen.
Here's an example (which had very fine divisions of income so we can see clearly what happens).
It's UK income data, taken to the log-scale of income:

Data from here ("Supporting tables" link)
(negative incomes and incomes above one thousand pounds per week are omitted)
The log income data was generated from the original table by randomly generating a very large sample from the given distribution of income uniformly in each income interval (then values below the centre of the leftmost interval were omitted before taking logs, because of the resulting distortions it produced if the very lowest values were retained). I did it this way because trying to do a plot of the log income directly from the original data had problems at the lower end.
The original claim would have this being normal on the left and exponential on the right. We see that the first part may not be too bad an approximation but we don't have enough of the right tail (which was truncated) to tell for sure whether the upper tail might be reasonably approximated by an exponential. 
We can see that we don't have an exponential on the left half for log-income. We might just have something approximately normal on the right (we can't rule it out because of the truncation), but if it is then it looks like it's at least a bit heavier than the left tail. 
Edit: It looks like the data used in this post could be the same data used to generate the plot used in Henry's post.
