Κατανομή
Συμβολισμός
Συνάρτηση πυκνότητας πιθανότητας
Παράμετροι
Μέση τιμή
Διακύμανση
Ομοιόμορφη
U
[
a
,
b
]
{\displaystyle {\mathsf {U}}[a,b]}
1
b
−
a
I
[
a
,
b
]
(
x
)
{\displaystyle {\frac {1}{b-a}}I_{[a,b]}(x)}
a
,
b
∈
R
{\displaystyle a,b\in \mathbb {R} }
(
b
>
a
{\displaystyle b>a}
)
a
+
b
2
{\displaystyle {\frac {a+b}{2}}}
(
b
−
a
)
2
12
{\displaystyle {\frac {(b-a)^{2}}{12}}}
Κανονική
N
(
μ
,
σ
2
)
{\displaystyle {\mathsf {N}}(\mu ,\sigma ^{2})}
1
2
π
σ
e
−
(
x
−
μ
)
2
2
σ
2
{\displaystyle {\frac {1}{{\sqrt {2\pi }}\sigma }}e^{\frac {-(x-\mu )^{2}}{2\sigma ^{2}}}}
μ
∈
R
,
σ
∈
R
+
∗
{\displaystyle \mu \in \mathbb {R} ,\sigma \in \mathbb {R} _{+}^{*}}
μ
{\displaystyle \mu }
σ
2
{\displaystyle \sigma ^{2}}
Εκθετική
E
x
p
(
λ
)
{\displaystyle {\mathsf {Exp}}(\lambda )}
λ
e
−
λ
x
{\displaystyle \,\lambda e^{-\lambda x}}
λ
>
0
{\displaystyle \,\lambda >0}
1
λ
{\displaystyle \,{\frac {1}{\lambda }}}
1
λ
2
{\displaystyle \,{\frac {1}{\lambda ^{2}}}}
Γάμμα
G
a
m
m
a
(
α
,
β
)
{\displaystyle {\mathsf {Gamma}}(\alpha ,\beta )}
β
α
Γ
(
α
)
x
α
−
1
e
−
β
x
{\displaystyle {\frac {\beta ^{\alpha }}{\Gamma (\alpha )}}x^{\alpha -1}e^{-\beta x}}
α
,
β
∈
R
+
{\displaystyle \alpha ,\beta \in \mathbb {R} ^{+}}
α
β
{\displaystyle {\frac {\alpha }{\beta }}}
α
β
2
{\displaystyle {\frac {\alpha }{\beta ^{2}}}}
Βήτα
B
e
t
a
(
α
,
β
)
{\displaystyle {\mathsf {Beta}}(\alpha ,\beta )}
Γ
(
α
+
β
)
Γ
(
α
)
Γ
(
β
)
x
α
−
1
(
1
−
x
)
β
−
1
I
(
0
,
1
)
(
x
)
{\displaystyle {\frac {\Gamma (\alpha +\beta )}{\Gamma (\alpha )\Gamma (\beta )}}x^{\alpha -1}(1-x)^{\beta -1}I_{(0,1)}(x)}
α
,
β
∈
R
+
{\displaystyle \alpha ,\beta \in \mathbb {R} ^{+}}
α
α
+
β
{\displaystyle {\frac {\alpha }{\alpha +\beta }}}
α
β
(
α
+
β
)
2
(
α
+
β
+
1
)
{\displaystyle {\frac {\alpha \beta }{(\alpha +\beta )^{2}(\alpha +\beta +1)}}}
Κωσύ
C
a
u
(
a
,
β
)
{\displaystyle {\mathsf {Cau}}(a,\beta )}
(
π
β
(
1
+
(
x
−
a
β
)
2
)
)
−
1
{\displaystyle \left(\pi \beta \left(1+\left({\frac {x-a}{\beta }}\right)^{2}\right)\right)^{-1}}
α
∈
R
{\displaystyle \alpha \in \mathbb {R} }
β
∈
R
+
{\displaystyle \beta \in \mathbb {R} ^{+}}
δεν υπάρχει
δεν υπάρχει
Weibull
W
e
i
(
α
,
c
)
{\displaystyle {\mathsf {Wei}}(\alpha ,c)}
c
α
x
c
−
1
e
−
x
c
α
{\displaystyle {\frac {c}{\alpha }}x^{c-1}e^{-{\frac {x^{c}}{\alpha }}}}
α
,
c
∈
R
+
{\displaystyle \alpha ,c\in \mathbb {R} ^{+}}
α
1
c
Γ
(
1
+
1
c
)
{\displaystyle \alpha ^{\frac {1}{c}}\Gamma \left(1+{\frac {1}{c}}\right)}
α
2
c
(
Γ
(
1
+
2
c
)
−
Γ
(
1
+
1
c
)
2
)
{\displaystyle \alpha ^{\frac {2}{c}}\left(\Gamma \left(1+{\frac {2}{c}}\right)-\Gamma \left(1+{\frac {1}{c}}\right)^{2}\right)}