# Negative Log Likelihood for AIC

I was looking at AIC, which is given by AIC = 2K - ln(L).

However, to my understanding, and observation, L = Log-Likelihood can be negative.

So in the case where L is negative, is AIC not applicable ?

Otherwise, ln(L) would give complex number, and I don't see complex number would be a useful value for this case.

• You seem to be confused by the definitions. If L is the likelihood (a product of probabilities, so to speak) it will be always positive. Then ln(L) is the loglikelihood, which can (and actially will, since 0$\leq$prob$\leq$1) be negative. And then it doesn't really matter what are the values of AIC themselves, only the differences matter. – corey979 Apr 1 at 10:40

Log-likelihood can be negative, indeed it will be if the likelihood is essentially a product of probabilities less than $$1$$. Thus $$-\ln(L)$$ will be positive, and so too will be $$2k-\ln(L)$$.
But the likelihood will be more than $$0$$, so the log-likelihood will be a real number.