Do you know how to normalize exponential distribution?

Do you know how to normalize exponential distribution?

Post by wu x » Sat, 26 Jul 2003 12:28:40



The data cluster at the lower bound of the scale--zero and decay to
the right. I tried box-cox, the zero's still cluster at the far left,
while other points become kinda symmetric. The transformed
distribution looks like the below :
  |  *              
  |  *           * *
  |  *         * *** *
  |  *       ***** ****
  |  *  *  * *  * ** ** * * **

My question is: is there a way to normalize it? How?Thanks.

 
 
 

Do you know how to normalize exponential distribution?

Post by Rich Ulric » Tue, 29 Jul 2003 05:55:27


 - posted and e-mailed.


> The data cluster at the lower bound of the scale--zero and decay to
> the right. I tried box-cox, the zero's still cluster at the far left,
> while other points become kinda symmetric. The transformed
> distribution looks like the below :
>   |  *              
>   |  *           * *
>   |  *         * *** *
>   |  *       ***** ****
>   |  *  *  * *  * ** ** * * **

> My question is: is there a way to normalize it? How?Thanks.

The appearance of the zeros at the left, followed by
a symmetrical curve, suggests to me that the X scores
fall into two parts.  

You can try to add information to get a new X.  That
assumes that the X  you have is proving to be an
inadequate surrogate for whatever it is intended to measure.

You can split the sample into two parts for analyses; that
is easier to justify if there is natural logic in making two parts.
That also seems to be the way you are going to provide a
concise summary of what you see, above, with X and Y.

If you have further analyses in mind, you can keep these
X and Y  scores as they are, and go on from there.  You
draw in  have the sort of far-outliers that really foul up the
statistical testing.

What are you trying to do with the X and Y?

--

http://www.pitt.edu/~wpilib/index.html
"Taxes are the price we pay for civilization."  Justice Holmes.

 
 
 

Do you know how to normalize exponential distribution?

Post by wu x » Tue, 29 Jul 2003 22:21:12




> - posted and e-mailed.

>> The data cluster at the lower bound of the scale--zero and decay to
>> the right. I tried box-cox, the zero's still cluster at the far left,
>> while other points become kinda symmetric. The transformed
>> distribution looks like the below :
>>   |  *              
>>   |  *           * *
>>   |  *         * *** *
>>   |  *       ***** ****
>>   |  *  *  * *  * ** ** * * **

>> My question is: is there a way to normalize it? How?Thanks.

>The appearance of the zeros at the left, followed by
>a symmetrical curve, suggests to me that the X scores
>fall into two parts.  

>You can try to add information to get a new X.  That
>assumes that the X  you have is proving to be an
>inadequate surrogate for whatever it is intended to measure.

>You can split the sample into two parts for analyses; that
>is easier to justify if there is natural logic in making two parts.
>That also seems to be the way you are going to provide a
>concise summary of what you see, above, with X and Y.

>If you have further analyses in mind, you can keep these
>X and Y  scores as they are, and go on from there.  You
>draw in  have the sort of far-outliers that really foul up the
>statistical testing.

>What are you trying to do with the X and Y?

``````````````

Thank you very much.

Y is the frequency of x values, as shown below. The tranformation is
log and square root, they show similar distribution.

*                                         *
**                                        *          
***                                       *           ***
*****                                    *          ** ***  
***********                            *         ********  
*******************                 *  * * ************* *  
The original distribution                      The transformed one

It's a scale in psychology. x can't be <0. Maybe that justify making
x=0 as a seperate group?

This variable will be entered as the dependent variable in a  ANOVA
factorial analysis.

 
 
 

Do you know how to normalize exponential distribution?

Post by Rich Ulric » Thu, 31 Jul 2003 03:49:39





> > - posted and e-mailed.


[snip, original, and mine]

Quote:

> >What are you trying to do with the X and Y?

> ``````````````

> Thank you very much.

> Y is the frequency of x values, as shown below. The tranformation is
> log and square root, they show similar distribution.

> *                                         *
> **                                        *          
> ***                                       *           ***
> *****                                    *          ** ***  
> ***********                            *         ********  
> *******************                 *  * * ************* *  
> The original distribution                      The transformed one

> It's a scale in psychology. x can't be <0. Maybe that justify making
> x=0 as a seperate group?

> This variable will be entered as the dependent variable in a  ANOVA
> factorial analysis.

I was not latching on to the idea that Y  showed the counts.
But I have new doubts about whether you should transform X.

The picture on the right looks worse in Fixed Font  than
in my variable-font,  and it looks worse than the original one.
Is there really anything wrong with the original, except for
being asymmetric?  

 - Is the extreme right prone to extra error in measurement?
 - Do you expect that the other variables under consideration
are not collinear with that graphical tail?  Those are reasons
to transform, to shorten the tail.  Is there a reason to do that?
Is there reason to do more than to truncate, at some
not-quite-so  extreme value?

--

http://www.pitt.edu/~wpilib/index.html
"Taxes are the price we pay for civilization."  Justice Holmes.

 
 
 

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TIA,

Wei
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