MATH 375 -- Probability and Statistics 1
Beta distributions
November 3, 2003
The beta pdf with parameters has the form
if 0 <= y <= 1
and 0 otherwise, where . Here
are some examples, using the BetaPDF function from
our Maple package.
> | read "/home/fac/little/public_html/ProbStat/MaplePackage/MSP.map"; |
Here is a typical shape:
> | plot([y->BetaPDF(6.7,2.3,y)],0..1,color=[red]); |
> |
Fixing and increasing shifts the location of the peak to the left, and narrows it
> | plot([y->BetaPDF(3,1,y),y->BetaPDF(3,3,y),y->BetaPDF(3,5,y),y->BetaPDF(3,7,y)],0..1,color=[red,blue,black,gray]); |
Fixing and increasing shifts the location of the peak to the right, and narrows it
> | plot([y->BetaPDF(1,3,y),y->BetaPDF(3,3,y),y->BetaPDF(5,3,y),y->BetaPDF(7,3,y)],0..1,color=[red,blue,black,gray]); |
Indeed, it is easy to see that the beta pdf with parameters and the
pdf with parameters have graphs that are reflections of one another
across the line (do you see why?)