In addition to @anon92994695’s excellent answer, also note that there is an infinite number of distributions; it’s just that some of them have a name and a parametric family for historical/convenience reasons. Any increasing function F: \mathbb{R} \to [0,1] (with some technical properties related to measurability) defines a distribution. People usually use “named” distributions/families as building blocks.
Depending on your problem, I would either recommend
- a simple transformation to the real line (eg with logit) and fitting (a family) of normals: this you can do directly with Distributions.jl, but you need to make sure there is no mass near the endpoints,
- a Bayesian approach.
What you end up doing will depend on how much you care about modeling your data correctly. If you are working at a company, I would suggest hiring a statistician do to this; otherwise read up on some methodology. Some recommendations in an earlier topic starting here: