# Can log likelihood funcion be positive [duplicate]

I have a mixture data. I used EM to estimate the model parameters. When I calculate the log likelihood function, I found that the values is positive. So, is that ok. Can the log likelihood function be positive?

To be more clear:

$ll = \sum_{n=1}^{N}\log(\sum_{k=1}^{K} \pi_{k} f(x_n;\theta_{k}))$

• To my understanding, likelihood function is usually a product of probabilities and log-likelihood is a sum of logs. Because probabilities are less than 1, theirs logs should be less than 0. And because you sum those logs, you should get a negative number. – Celdor Dec 21 '17 at 10:32
• The comment above is wrong. The likelihood function of continuous parameters (such as your case, I guess) is based on probability densities, which can be greater than 1 depending on the domain and the density, so the log likelihood can occasionally be positive. Still, you should check that everything else is correct. – lacerbi Dec 21 '17 at 10:35
• yes, my density is continuous. ' – Alice Dec 21 '17 at 10:37