Many groups with a single large element and a lot of small ones - How to assess?

Question

I have a sample of 100 groups, each with 50 elements. All elements in each group are characterized with a single "size" value.

The sizes of all the elements in a group (with 50 elements) are normalized by dividing them with the size of the maximal element (in their group, regardless of the other 49). Hence I have 100 groups, each with at least one element at size 1 (which constitute the maximal element or elements) and the rest are smaller.

Observing the data (manually), I notice that in the majority of groups (96 of them) there is a characteristic distribution of sizes : there always exist either a single or two large element (larger than 0.85) and the rest of the sizes are smaller than 0.3.

Now, I wonder (and would appreciate suggestions :-) of what would be the right statistical tool to generalize this phenomenon and make claims on the probability that this is the prevailing distribution of elements within any group in the population.

Thanks!

Answer 1

Here are some ideas to start with :

1. Kullback–Leibler divergence allows to measure distances between probability distributions. Hence it is possible to measure a distance between the given distribution and any artificially generated other distribution(e.g. uniform).
2. Bootstrapping - will allow the assessment of different variables in the sample (e.g its variance).
3. Permutation analysis - Take all samples (100 X 50) and reshuffle (permute) them many times. Assess in what percentage of the re-sampled data does the phenomenon reoccur.