# Common Continuous Distributions with [0,1] support

## Question

I am looking to understand what possible common statistical continuous distributions exist with support [0,1].

## Background

In my work I often come across data which are bounded between 0 and 1 (both inclusive) and likely skewed to the right.

This data mainly consist of sales converted into percentages between 0 and 1, by either calculating total per cent of sales or conversion (sales divided by page views).

As I am not very proficient in statistics, I always struggle to find the best distribution to explain this data.

Wikipedia has a list of distributions supported on an interval

Leaving aside mixtures and 0-inflated and 0-1 inflated cases (though you should definitely be aware of all of those if you model data on the unit interval), which ones are common would be hard to establish (it will vary across application areas for example), but the beta family, and the triangular, and the truncated normal would probably be the main candidates as they seem to be used in a variety of situations.

Each of them can be defined on (0,1) and can be skewed either direction.

One example of each is shown here:

That they’re often used doesn’t imply they’ll be suitable for whatever situation you’re in, though. Model choice should be based on a number of considerations, but where possible, theoretical understanding and practical subject area knowledge are both important.

I always struggle to find the best distribution to explain this data.

You should get away from worrying about “best”, and focus on “sufficient/adequate for the present purpose”. No simple distribution such as the ones I mentioned will really be a perfect description of real data (“all models are wrong…”), and what might be fine for one purpose (“… some are useful”) may be inadequate for some other purpose.