Gamma
The Gamma distribution is
defined for x > 0 by the
integral
where
Γ
t
=
e-uut-1du is the
Gamma function. The parameters a and b are called the shape parameter
and scale parameter, respectively. The mean of this distribution is ab and
the variance is ab2. The probability density function for the gamma
distribution is
GammaDen(
u;
a,
b) =
ua-1e-
The following plots show cumulative distribution functions
GammaDist
x;a, b
and probability density functions
GammaDen(x;a, b) for
(a, b) =
1,.5
,
1, 1
,
2, 1
and
0≤x≤4.
itbpFU2.1577in1.7573in0inGamma density functions itbpFU2.1577in1.7573in0inGamma distribution functions