Central Limit Theorem for Mode

[square173205]

Central limit theorem is for the mean value of distribution. However

not only the mean value but also the mode might follow similar limit

theorem. I tried to prove it in the following site with experimental

verification using Java applet;

 

http://hecoaustralia.fortunecity.com/mode1/clt-mode.htm

[insane_alien]

update your java dude.

[uncool]

Can you state the "central limit theorem" for the mode in mathematical terms?

=Uncool-

[Bignose]

I couldn't get the java to work either, but just from the text of your post, I'd like to make one comment. But, just using "experimental verification" is insufficient for proof. As uncool stated, you need to show it in mathematical terms. Intuitively, there is probably some sort of central limit theorem for modes, but intuition can often be wrong, that's why formal proof is needed and not just "experimental verification".

[square173205]

I couldn't get the java to work either, but just from the text of your post, I'd like to make one comment. But, just using "experimental verification" is insufficient for proof. As uncool stated, you need to show it in mathematical terms. Intuitively, there is probably some sort of central limit theorem for modes, but intuition can often be wrong, that's why formal proof is needed and not just "experimental verification".

 

I'm a little confusing for I wonder whether you've not seen my website. Certainly I've put the link for the proof in my website..

[insane_alien]

where the proof is supposedly embedded in a steaming pile of crap antiquated java that doesn't display on anything no matter what version of java is used(i have tried).

[square173205]

Central limit theorem is for the mean value of distribution. However

not only the mean value but also the mode might follow similar limit

theorem. I tried to prove it in the following site with experimental

verification using Java applet;

 

http://hecoaustralia.fortunecity.com/mode2/clt-mode2.htm

 

(I've posted the similar case before, in which the density around the

mode was in C^2 class. This time the density at the mode is not

smooth. Then I found the limit distribution is different from Gaussian

curve.)

[YT2095]

threads merged...

[insane_alien]

still in a steaming pile of java that doesn't work.

[Bignose]

I'm a little confusing for I wonder whether you've not seen my website. Certainly I've put the link for the proof in my website..

 

I tried to view your website, as insane_alien said, I couldn't get it to work.

 

Nevertheless, my main point is that without a formal proof, it doesn't matter how many examples you create, that isn't "proof". There is a formal proof of the central limit theorem, any good book that goes beyond introductory statistics and probability will have it. Or you can look at http://mathworld.wolfram.com/CentralLimitTheorem.html for a proof.

 

If you can provide something similar to this same level of rigor, then you've got something. Just a bunch of examples has a little meaning, but nothing conclusive. Log on to Amazon.com, and search for "counterexamples in probability" and there are no less than three different books that a full of examples where "intuition" is dead wrong. Intuition can be valuable, but it can also be exceptionally misleading. That's why rigorous proofs are needed, not just examples, even if there are a lot of examples.