Re: [Phys-l] Basic statistics

[Bernard Cleyet <bernardcleyet@redshift.com>]

got it:

http://physics.ucsc.edu/~drip/133/ch2.pdf

vide p.8, ff.


ch3.pdf and ch4.pdf  may also be of interest.

bc, for 13 years managed 133 (and 134), including editing and publishing 
the manuals.


Bernard Cleyet wrote:

> Yes, I was confused -- thinking of an example Peter Scott wrote of an 
> example re. the CLT, which I haven't yet found, if, later.
>
> bc
>
> Jack Uretsky wrote:
>
>  
>
> > Single or multiple makes no difference.  His statement is still correct. 
> > I suggest you check a statistics text and review the proof.
> >
> > I've just checked the Handbook, and it appears that Wipedia is correct. 
> > However it does not approach n(0,1), as other distributions do.
> >
> > On Sat, 11 Nov 2006, Bernard Cleyet wrote:
> >
> >
> >
> >    
> >
> > > I think you two are "talking (writing) past each other".    One is a
> > > single distrib. tother several independent.  Furthermore, Wiki, claims
> > > that the Chi-square also does tend towards normalcy, but VERY slowly, as
> > > the # of DOF increases.
> > >
> > > http://en.wikipedia.org/wiki/Chi-square_distribution
> > >
> > >
> > > bc
> > >
> > >
> > >
> > >
> > >
> > > Jack Uretsky wrote:
> > >
> > >   
> > >
> > >      
> > >
> > > > As already pointed out, the central limit theorem does not apply to all
> > > > distributions.  You must state the theorem carefully.  In the case of the
> > > > chi-square distribution it is easy to demonstrate by example with MathCad
> > > > or a similar program that the large N limit is not Gaussian.
> > > > 					Regards,
> > > > 						Jack
> > > >
> > > > On Fri, 10 Nov 2006, Polvani, Donald G. wrote:
> > > >
> > > >
> > > >
> > > >     
> > > >
> > > >        
> > > >
> > > > > Jack Uretsky wrote:
> > > > >
> > > > >
> > > > >
> > > > >       
> > > > >
> > > > >          
> > > > >
> > > > > > This is a misconception. There are many distributions that become
> > > > > >
> > > > > >
> > > > > >         
> > > > > >
> > > > > >            
> > > > > Gaussian in the large N limit, but not all.
> > > > >
> > > > >
> > > > >       
> > > > >
> > > > >          
> > > > >
> > > > > > The chi-squared distribution is an example of one that does not.
> > > > > >
> > > > > >
> > > > > >         
> > > > > >
> > > > > >            
> > > > > However, for the SUM of independent, identically distributed random
> > > > > variables, each with mean mu and variance sigma^2, the central limit
> > > > > theorem tells us that the distribution (of the sum) tends to a Gaussian
> > > > > as N approaches infinity.
> > > > >
> > > > > Don Polvani
> > > > > Northrop Grumman Corp.
> > > > > Undersea Systems
> > > > > Annapolis, MD 21404
> > > > > _______________________________________________
> > > > > Forum for Physics Educators
> > > > > Phys-l@carnot.physics.buffalo.edu
> > > > > https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
> > > > >
> > > > >
> > > > >
> > > > >       
> > > > >
> > > > >          
> > > >     
> > > >
> > > >        
> > > _______________________________________________
> > > Forum for Physics Educators
> > > Phys-l@carnot.physics.buffalo.edu
> > > https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
> > >
> > >   
> > >
> > >      
> >
> >
> >    
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