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Subject: Re: Can PDF be more than one??
Date: Wed, 22 Sep 2010 19:09:04 +0000 (UTC)
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"kumar vishwajeet" <kwzeet@gmail.com> wrote in message <i7d64l$36e$1@fred.mathworks.com>...
> Can anyone tell me whteher Probability density function can be more than one. In my opinion, it can be.Because PDf is the derivative of Probability distribution function with respect to change in random variable. If the change in the distribution function is more than the change in the corresponding value of random variable, the PDF will be more than one. Am I correct??
> I am asking this question with relevance to Lorenz System. I am trying to plot the pdf of this system. After some time the PDF orient themselves in a particular direction thus streching more in that direction. The value of the peak, meanwhile, goes beyond one reaching upto 6 and then suddenly drops to less than one and keeps on dropping till it becomes almost zero (10^-126).Is this a normal behavior for the PDf of a Lorenz System?/
> 
> Thanks
- - - - - - - - - - -
  When you say "Lorenz System" do you refer to the Cauchy-Lorentz distribution?  With a variable scale parameter, that pdf can certainly exceed one - just have the "scale factor" less than 1/pi.  See the site:

 http://en.wikipedia.org/wiki/Cauchy_distribution

  If you refer to the "Lorenz attractor" with its system of three ordinary differential equations which can exhibit chaotic behavior, there doesn't seem to be any probability density function associated with it.  It is a deterministic system.  Can you be more specific about what you mean by the "Lorenz System".

Roger Stafford