5
$\begingroup$

I am trying to model a distribution, on the number of occurrences of an event in a 24 hour time span.

Right now, I discretize the 24 hour time span into hourly intervals, and each hour is taken as a categorical outcome, and I count the number of occurrences of the event in each hour (outcome). Hence, this problem is modeled as a multinomial distribution.

As time is a continuous variable, is there a continuous version of multinomial distribution? That is, I can count the number of occurrence of the event in the continuous outcome(time).

$\endgroup$
  • $\begingroup$ Why a multinomial distribution? Is there a fixed total number of occurances? The logical model to use would be a Poisson process. Anyway, the continuous analogue of the multinomial distribution is the multivariate normal distribution. $\endgroup$ – Raskolnikov Mar 2 '12 at 22:32
3
$\begingroup$

A similar distribution would be the Dirichlet distribution.

A random sample of a Dirichlet distribution is a set of probabilities that add to one. You can then multiply each by, say, $24$, to get a "continuous multinomial distribution."
This is just a direct answer to your question about "continuous multinomial distribution", whether you should use it to model your data is another question.

$\endgroup$

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.