Let me leave aside your wish to keep the data 'grouped' for the moment (I will return to it). You have *interval censored* data. https://en.wikipedia.org/wiki/Censoring_(statistics)#Types You could fit either distribution by maximum likelihood; it's a matter of writing the likelihood for the censored data and maximizing it. The obvious start values to use would be the ML estimates you get by just placing all the data at the center of each interval. The full ML estimates will be very likely to only differ slightly from those so convergence should be only a step or two. The likelihood could be written in grouped form using the counts, so grouped or ungrouped should not be a big issue. Alternatively you may be able to use parametric survival regression models to do get ML estimates without even having to write that censored likelihood at all (at the cost of having some small additional setup for the data). Not every implementation of such models will work with just the counts in each bin though; some may assume you have individual data (though it shouldn't be hard to check). --- If you would be happy with an approximate (asymptotically efficient) answer, it's simple enough to write the goodness of fit for either model in terms of a chi-squared statistic and use minimum chi-squared estimation. https://en.wikipedia.org/wiki/Minimum_chi-square_estimation Berkson's paper (which is listed in the Wikipedia article) does a good job of explaining its usefulness and simplicity. (If you replace that Pearson chi-squared with the G-statistic I think you should get back to ML estimates.)