# Thread: Question on maximum likelihood

1. ## Question on maximum likelihood

F(x) = O x^(O-1),
( O is theta)

derive the max. likelihood funciton

ln L = ln O + (O-1) lnx

d ln L/dO = 1/O + (O-1)/X

this is as far as i could reach, could someone show me the steps from here?

Q2) F(x) = 1/ (2MR^2)1/2 e^(X^2 / (2MR^2)

(M is Pie, and R = Sigma)

ln L = ( -1/2 ln 2M - 1/2 ln R + X^2/2R^2)
d ln L/ dR = ( -1/2R + X^2/2R^2)
= n/R + summation of X^2/ R^2 = 0
hence
R = X^2/n

is this right?

I would appriciate it if someone could confirm this answer and show me the steps in the previous question!

2. d ln L/dO = 1/O + (O-1)/X
are you differentiating by O or X ? Check this

Once you find d ln L/dO then solve this equation d ln L/dO =0 and solution is estimate of O.

And are you assuming only one observation for the estimation?

3. ah man, isee what your sayin, i think i made an error there:
ln L = ln O + (O-1) lnx
d ln L/dO = 1/O + O
we equate this to 0,
and then:
(1-O^2)/O= 0
O = Root 1?

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