Information Technology Reference
In-Depth Information
2
Γ
((
k
+1)
/
2)
Γ
(
k/
2)
2
V
:
k
−
.
H
:ln
Γ
2
+
2
k
1)
ψ
2
.
−
ln 2
−
(
k
−
4. Chi-Square distribution.
PDF:
f
(
x
;
k
)=
1
2
k/
2
Γ
(
k/
2)
x
k/
2
−
1
e
−x/
2
;
x
≥
0
,k>
0.
V
:2
k.
H
:
2
ψ
2
.
Comment: a special case of the Gamma distribution.
2
+ln2+ln
2
+
1
k
k
−
5. Erlang distribution.
PDF:
f
(
x
;
k, λ
)=
λ
k
x
k
−
1
e
−
λx
(
k−
1)!
;
x
≥
0;
k, λ >
0.
V
:
k/λ
2
.
H
:(1
k
)
ψ
(
k
)+ln
Γ
(
k
λ
+
k
.
Comment: a special case of the Gamma distribution.
6. Exponential distribution.
PDF:
f
(
x
;
λ
)=
λe
−λx
;
x
−
≥
0;
λ>
0.
V
:1
/λ
2
.
H
:1
ln
λ
.
Comment: a special case of the Gamma distribution;
H
(
V
) is also USF
for the generalized exponential distribution (see Pearson type X).
−
7.
F
distribution.
PDF:
f
(
x
;
d
1
,d
2
)=
(
d
1
x
)
d
1
d
d
2
2
(
d
1
x
+
d
2
)
d
1
+
d
2
1
/x
B
(
d
2
,
d
2
)
;
x
≥
0
,d
1
,d
2
>
0.
2
d
2
(
d
1
+
d
2
−
2)
V
:
d
1
(
d
2
−
2)
2
(
d
2
−
4)
;
d
2
>
4.
H
:ln
d
1
d
2
B
d
2
,
d
2
+
1
d
2
ψ
d
2
1+
d
2
ψ
d
2
+
−
−
+
d
1
+
d
2
ψ
d
1
+
d
2
.
Comment: a special case of Pearson Type VI.
8. Gamma distribution.
PDF:
f
(
x
;
k, θ
)=
x
k−
1
e
−x/θ
/
(
θ
k
Γ
(
k
));
x>
0;
k, θ >
0.
V
:
kθ
2
.
H
:
k
+ln
θ
+ln
Γ
(
k
)+(1
− k
)
ψ
(
k
)
.
9. Gauss distribution.
PDF:
f
(
x
;
μ, σ
)=
√
2
πσ
e
−
(
x
−
μ
)
2
1
2
σ
2
;
x
∈
R
.
V
:
σ
2
.
H
:ln(
σ
√
2
πe
).
10. Generalized Gaussian distribution.
PDF:
f
(
x
;
α, β, μ
)=
2
αΓ
(1
/β
)
exp
−
/α
)
β
;
x
β
(
|
x
−
μ
|
∈
R
;
α, β >
0.
α
2
Γ
(3
/β
)
Γ
(1
/β
)
V
:
.
ln
β
2
αΓ
(1
/β
)
.
1
H
:
β
−
