# The Value of Likelihood Function (Basic Question)

Here is my question:

1. Can the value of 'likelihood' function take the value that is greater than 1? If yes, how can we mathematically show that?

[ I know that the likelihood function is not the probability density function and its value can be greater than 1, but I want to show my claim more properly.]

2. When we scale the data (such as the bond yields) by multiplying 100*data, how does this operation affect the 'log-likelihood' function comparing with the case of dividing the data by 100 ((1/100)*data)?

Thank you very much for your time and considerations. Sp

• 1. This reads rather like homework/coursework. Is it for some subject? 2. Your first question is addressed by several posts already on site, but follows directly from the definition of likelihood and facts you've already stated. Commented Sep 3, 2020 at 5:10
• @Glen_b Hi Glen, This is not homework. It is a comment from a referee. Some of them asked me why the value of log-likelihood is positive and that is why I am trying to find an example of this to verify my claim. Anyway, thank you for your reply. Commented Sep 3, 2020 at 5:17
• On the first question, see the links provided here, for example: stats.stackexchange.com/questions/319859/… -- searches turn up more. I suggest you edit to focus on the second question Commented Sep 3, 2020 at 5:23
• An example is easy! Take a normal distribution with small $σ$, like $σ=0.1$ say, and any sample size you like, and look at the likelihood for $\mu$. Or likelihood for $\theta$ in a uniform on $(0,\theta)$ where the largest observation is less that $\frac12$. Commented Sep 3, 2020 at 5:26