Can likelihood intervals be negative?
Likelihood must be at least 0, and can be greater than 1. Consider, for example, likelihood for three observations from a uniform on (0,0.1); when non-zero, the density is 10, so the product of the densities would be 1000. Consequently log-likelihood may be negative, but it may also be positive.
Can confidence level be negative?
The 95% confidence interval is providing a range that you are 95% confident the true difference in means falls in. Thus, the CI can include negative numbers, because the difference in means may be negative.
Is the argument of the log going to infinity?
The argument of the log is going to infinity and so the log must also be going to infinity in the limit. The answer to this part is then, First, note that the limit going to negative infinity here isn’t a violation (necessarily) of the fact that we can’t plug negative numbers into the logarithm.
Do you need a right hand limit to go to infinity?
Remember that in order to do this limit here we do need to do a right-hand limit. So, the exponent goes to infinity in the limit and so the exponential must also go to infinity. Here’s the answer to this part.
What happens when the limit is negative infinity?
Let’s start this one off in the same manner as the first part. Let’s take the limit of each of the pieces. This time note that because our limit is going to negative infinity the first three exponentials will in fact go to zero (because their exponents go to minus infinity in the limit).
What’s the difference between plus infinity and minus infinity?
So, the only difference between these two limits is the fact that in the first we’re taking the limit as we go to plus infinity and in the second we’re going to minus infinity. To this point we’ve been able to “reuse” work from the first limit in the at least a portion of the second limit.