I apply MLE method in the attached file.
I wrote the code for implementation MLE. After that I run with their example but I got different result for k.
Could anyone help me check the equation 26 in this paper? or tell me why I cannot have the same results?
Another problem is when I got k's value, I went back to equation 25 but the value of f(k) is not equal zero.
Please help me.
Thanks all.
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do not follow blindly the equations given in the papers !
if you take f(k) as defined by (25), then (26) is just wrong, but you can compute the right derivative yourself !
seems to me that (26) gives the derivative of the function F(k) = f(k) * SUM(xi^k)
(with f(k) defined as in (25) ; F(k) is slightly simpler for the computation of the derivative as you get rid of the denominator)
and indeed, solving f(k) = 0 or F(k) = 0 leads to the same solution but for Newton Raphson, you have to use either f(k)/f'(k) or F(k)/F'(k) ...not f(k)/F'(k) !
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Tran, look the computations.
I have kept 16 digits accuracy.
You have to be careful with what you read!
Nice exercise...
Dear Fabrice Clerot and Demetris Christopoulos,
I had a stupid question :(. Thanks for your answers.
I have another question. If k=1.908... => f(k) =0.1555.... I think f(k) must be close to zero, why is it still large?
I try to loop many times (more than 1000 times). It stills the same.
Thanks all.
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