3
$\begingroup$

Similar questions to this

Common name for distributions that are bounded on one side

I am looking for common name or an exhaustive list of which distributions are bounded on both sides [0,1]. This is because my data is similar to this (cannot be less than 0 and greater than 100). I need to fit a distribution to this data. In order to do this, I need to firs find a list of distributions that are bounded on both sides and try them one by one to see which distribution closely resembles my data.

$\endgroup$
  • 2
    $\begingroup$ There is no exhaustive list. Think of this: any nonnegative function with finite integral on [0,1] can be a density function. You can't name them all. $\endgroup$ – Aksakal Mar 14 '18 at 14:19
  • $\begingroup$ Okay. Is there a list of some commonly used family of distribution that I can fit to a bounded dataset $\endgroup$ – 89_Simple Mar 14 '18 at 14:26
  • $\begingroup$ Have a look at beta regression and if you analyze your data in R, the betareg package is very useful. Also searching for beta regression on this site will give you a lot of examples. Note however, that if your data has zero and ones, the analysis won't run. In this case, you can scale your data so it will fall between 0 and 1. There is a scaling procedure mentioned in the PDF (page 3, 3rd paragraph). $\endgroup$ – Stefan Mar 14 '18 at 15:42
2
$\begingroup$

There's no one universal list, and there can't be an exhaustive list. However, you can find a list of some continuous densities with bounds in wiki: https://en.wikipedia.org/wiki/List_of_probability_distributions#Supported_on_a_bounded_interval

Also, remember that you can take any distribution and bound it in an interval. These are called truncated distributions, e.g. see truncated normal.

$\endgroup$
  • $\begingroup$ Thank you. I was not aware of the truncated distribution. I will read around it. $\endgroup$ – 89_Simple Mar 14 '18 at 14:32
0
$\begingroup$

Check out the kernel functions. When a kernel satisfies $$\int_{-\infty}^\infty K(x)\,\mathrm dx = 1,$$ it results in a probability density function.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.