Hello,
Let a n-sample following a Pareto distribution.
Then the likelihood function, which is the pdf of the n-tuple, will be :
So the log is
now differentiate with respect to ...
Same thing for the other one.
I'm having some trouble finding the log-likelihood in these questions:
Question 1
Pareto distribution is:
f(yt) = θ / (yt ^ (1+θ))
What is the log-likelihood, log L (θ)
Question 2
Geometric distribution:
f (yt) = θ (1 − θ)^yt, yt = 0, 1, 2, · · ·
where θ > 0, is an unknown parameter. Let {y1, y2, ..., yT } be iid observations from the geometric distribution.
What is the log-likelihood?
I also need to take derivatives of both. Would appreciate some help, I'm stuck!