MATH 375 -- Probability and Statistics 1
Some gamma probability density functions
October 28, 2005
A continuous random variable is said to have a
gamma distribution with parameters , if its
pdf has the form: f( y ) = if y > 0
0 if y <= 0
Here are some Gamma pdf graphs. Note that the maximum
shifts to the right and the peak value decreases as increases.
In the special case , the pdf is actually always decreasing for y > 0.
> | f:=(y,alpha,beta)->y^(alpha-1)*exp(-y/beta)/(GAMMA(alpha)*beta^alpha); |
= 1 :
> | plot(f(y,1,1),y=0..10); |
, :
> | plot(f(y,2,1),y=0..10); |
, :
> | plot(f(y,3),y=0..10); |
, :
> | plot(f(y,5),y=0..20); |
> |