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pddxt@chalk.cpceng.cpc.gmeds.com (Dino Triantos 575-4386) writes:

>I'm working on a problem in Mood, Graybill and Boes that asks to find the
>relationship between the F and Beta distributions.  The problem asks:  If 
>X has an F distribution with m and n degrees of freedom, show that
> 
>		        mX/n
>		 W =   -------       has a Beta distribution.
>		      1 + mX/n

>Any suggestions or solutions would be greatly appreciated! 

>Dinos Triantos
>GM/Midsize Automotive Division 
>Vehicle Systems Analysis
>C-P-C Engr. Center Rm# G241
>Fax: (313) 575-7270
>E-mail: pddxt@cpceng.cpc.gmeds.com

Is this a homework problem or will the solution to this
statistical issue help GM build better cars?  The net has
informal prohibitions against providing answers to homework
problems.  The problem you raise is a very standard homework
assignment in undergraduate statistics classes.  When I did it as
a homework problem many years ago I remember that it was a bit
easier to do it as W = 1/(1+(m/n)F).  It won't help you solve it,
but a useful insight is that W is often known as R^2.  Good luck!

gary mcclelland
univ of colorado
mcclella@yertle.colorado.edu

In article <1993Jan21.181433.8679@mloeff01.cpchq.cpc.gmeds.com>
pddxt@chalk.cpceng.cpc.gmeds.com (Dino Triantos 575-4386) writes:
 
>
>I'm working on a problem in Mood, Graybill and Boes that asks to find the
>relationship between the F and Beta distributions.  The problem asks:  If
>X has an F distribution with m and n degrees of freedom, show that
>
>		        mX/n
>		 W =   -------       has a Beta distribution.
>		      1 + mX/n
>
>Any suggestions or solutions would be greatly appreciated!
>
>Dinos Triantos
>GM/Midsize Automotive Division
>Vehicle Systems Analysis
>C-P-C Engr. Center Rm# G241
>Fax: (313) 575-7270
>E-mail: pddxt@cpceng.cpc.gmeds.com
Try the change of variables x = nu2/(nu2 + nu1F), where F is the F
variate.  Kendall & Stuart (1963) have such an exercise too.