I am trying to find the maximum likelihood estimator of a random sample where X~BIN(1,p). I am stuck trying to find the natural log of a permutation. Please help!

  • $\begingroup$ Express the permutation in factorial form, then replace factorial with Gamma function. LnGamma is a common function for stats programs (even Excel) to provide. $\endgroup$ – tristan Feb 26 '14 at 20:50

This grew too long for a comment, so I guess it's an answer:

Your question has a number of problems and must be edited.

(1) A permutation is essentially a rearrangement, a reordering of objects. You can't take the log of a rearrangement. When you say "log of a permutation", you presumably want to take the log of a quantity -- a number. You should specify (in your question via an edit) what that quantity actually is. Is it a count of permutations, or even a count of combinations, for example? Please be explicit.

(2) You don't find MLE's of samples, you find MLEs of parameters. Which parameter? $p$, maybe? Again, please edit your question to be explicit.

(3) This appears to be routine textbook-style question. Please read the link carefully, and add the tag to your question (you'll also need to make edits to your question to fit the guidelines for this type of question - specifically, to show your work and explain exactly where you ran into difficulty). Is this for some subject?

Now to address the essence of the question:

a) If you it is $p$ you want the MLE for, you don't need to take to compute the log of some count of whatever quantity that's out the front in the pdf. Just leave it as $\log(\text{<whatever>})$. It doesn't contain $p$ and will become a non-issue as soon as you take derivatives.

b) If you actually evaluate that quantity (the term you want to take logs of) for this particular example, it's a nonissue in any case. (Work it out and you'll see why.)

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