Graphics Programs Reference
In-Depth Information
Some Common
Probability Densities
Appendix 13B
Chi-Square with N degrees of freedom
(
N
⁄
2
)
1
x
2
x
f
X
()
=
-------------------------------
exp
-----
;
x
>
0
2
N
⁄
2
Γ
N
(
⁄
2
)
σ
2
XN
=
;
=
2
N
∞
∫
Γ () λ
z
1
λ
;
gamma function
=
=
e
d
λ
Re
{} 0
>
0
Exponential
(
f
X
()
a
=
exp
{}
ax
)
;
x
>
0
1
---
1
a
2
σ
2
X
=
;
=
-----
Gaussian
xx
m
σ
2
1
2πσ
1
---
σ
2
σ
2
----------
--
--
--------------
;
f
X
()
=
exp
X
=
;
=
m
Laplace
σ
---
f
X
()
=
exp
{
σ
xx
m
}
659
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