1
$\begingroup$

I have an ordinal random variable {0,1,2,3}. The variable should describe disease severity. What kind of probability distribution is the best fit to model this variable?

The categorical distribution does not account for an inherent order.

$\endgroup$
1
  • 3
    $\begingroup$ This sounds like an ordinal regression $\endgroup$
    – Onyambu
    Commented Dec 20, 2021 at 9:38

1 Answer 1

1
$\begingroup$

A probability distribution assigns probabilities to events, whether these carry additional structure (like an ordering) or not.

Look at it this way: if your random variable gave some number of events, then there would also be a natural ordering on 0, 1, 2, ... events. If there is some upper limit to the possible number of events, we end up pretty exactly in your situation. There is still no need to account for the ordering in the probability distribution considered.

You have a finite number of possible events, and any discrete distribution would be appropriate.

Conversely, in modeling your data, you should take the structure into account. As Onyambu notes, something like ordinal regression would be appropriate.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

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