Fitting data sample to a distribution I'm trying to fit a data sample to a distribution.  So far I have created a histogram and fitted the data with a lognormal distribution in R and made a Q-Q plot in excel (of log(benefits paid) against theoretical normal quantiles).
Here are my histogram and Q-Q plot:


However, I don't think this distribution is fitting the data closely enough.
I was hoping for an opinion on whether there are any distributions which should fit the data better.  Or is this as closer fit as I'm going to be able to get?
 A: Have you tried a gamma distribution? That is a little more flexible than a log-normal and typically has thinner tails, which appear to be where your fit is lacking. 
If that doesn't work, you might want to click through this list on wikipedia. There are many choices for distributions with positive support, and of course each one has it's pluses and minuses depending on your application. It looks like you're doing something with financial data, so the Pareto distribution may also be worth exploring. That tends to have thick tails though so maybe try the gamma first. 
A piece of advice though: you're not going to find a closed-form distribution that fits your data perfectly. Different distributions will miss in different ways, so you'll need to ask yourself exactly how good and where in the distribution the fit has to be. The log-normal fit in your pictures may not actually be that bad depending on your priorities. If you're doing regression analysis, then maybe it works. If you're modeling tail-risk, then maybe not. Also, do you really need a closed form distribution? If distribution fit qua fit is your goal, then maybe the empirical distribution is the way to go.
A: The bins in your histogram are a bit too wide (the default has too few bins), making it hard to discern the shape clearly. 
The QQ-plot suggests that a finite mixture of perhaps two or three components, possibly of something right skew, perhaps like gamma distributions.
