Processing math: 100%
Google
 
Web unafbapune.blogspot.com

Sunday, January 12, 2014

 

Infinity Entropy

What would be a good example of an infinite entropy ? Let
  p(x)=1Axlog2xwhere A=x1xlog2x
Note A converges as 1xlog2xdx=1logx. Now,
  H(X)=xp(x)logp(x)=x1Axlog2xlog1Axlog2x=xlog(Axlog2x)Axlog2x=x[logAAxlog2x+logxAxlog2x+loglog2xAxlog2x]=x[logAAxlog2x+1Axlogx+loglog2xAxlog2x]
But the middle term (in blue) diverges, as 1xlogxdx=loglogx. Hence H(X) diverges.

Source: math.stackexchange.com.


Comments: Post a Comment

<< Home

This page is powered by Blogger. Isn't yours?