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MLE for Gamma Distribution

G

Goku

Member
Hi guys!

With regards to estimation, does anyone know how to derive the MLE for a Gamma Distribution? I can only derive the Moment-based estimates.

:confused:
 
I'm really not in the mood for trying it out myself, but most of the time when the log pdf is not differentiable, the MLE does not exist.

Cheers.
 
Hi Erik!

Thanks for the reply. You're right in pointing out that the MLE's for certain ln{ L(X) }'s can not be integrated. An ideal example in this case is the Gamma Distribution. However, what perturbs me is that the Core Notes state it can be found; in particular, by making a specific substitution...(its just before Question 3.11 in the Core Reading or CMP). On making the substitution, not much is changed with regards to the integration.

Another question I have is whether the probability densities or cdf's are provided,regarding all densities that we are required to know for the exam. Also, is the MGF provided, as well as the mean and variance?
 
Everything that exists in enclosed form can be found in the gold tables. You should get a copy of this if you don't have one already in order to familiarise yourself with it. It can save a lot of time in the exam if you know where everything is.

The only thing that is not in the table is the cumulant generating function. This is just
ln(mgf)
and is useful to find the skewness of a distribution quite easily. The term before t^r/r! in the series expantion is the r'th cumulant and the first cumalant is the mean, the second the variance and the third is the skewness. This helped me a lot in CT6.

Don't waist too much time on the gamma MLE. There are more important topics to spend time on. In the exam you'll probably get an easier MLE.

Good luck.

Erik
 
Gold Tables?

Hey Erik!

Gold tables? I've heard about the "tables" but what are the gold tables and how do I obtain them?

Regarding the topic of this thread, well, just for interest, the MLE can be found for the Gamma Distribution hey! My intuition tells me that the change of variables method will work due to the result: The MLE of a Function is the Function of the MLE's . I only realised this this weekend after doing some Q's.

Anyway, good luck with the studying!
 
The gold tables are the tables. You can buy them from the Institute, the order form is on their website.
 
They are actually yellow. But everyone talks about the gold tables. An older version of it was green, thus the colour coding!

Good luck
 
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