Can the likelihood take values outside of the range [0, 1]? [duplicate]

I got a log-likelihood value of -34.82, so I am not getting whether the answer which I have got is right or not.

Can the likelihood take values outside of the range [0,1]?

Answer

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.

[Indeed, according to some definitions the likelihood is only defined up to a multiplicative constant (e.g. see here), so even if the density were bounded by 1, the likelihood still wouldn’t be.]

Attribution
Source : Link , Question Author : Community , Answer Author : Glen_b

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