___________________________________________________________________________________
Bernard Clément, PhD 2003
D I S T R I B U T I O N S
Nom Paramètres Domaine Masse / Densité Moyenne Variance
DISCRÈTES
BERNOUILLI 0≤θ≤1 0 ,1
θ
X( 1
−θ )
1−X θ θ(1−θ)BINOMIALE 0 1 ...
, 2 , 1
≤
≤
= θ
n 0,1,...,n x n x
x
n −
−
θ (1 θ) nθ nθ(1−θ)
GÉOMÉ-
TRIQUE 0<θ <1 1,2,... θ(1−θ)X−1
θ 1
2
1 θ
θ
−
PASCAL 1,2,...
1 0
=
<
<
n θ
...
, 1 ,r +
r r x r
r
x −
−
−
− (1 )
1
1 θ θ θ
1
2
) 1 (
θ θ
− r
HYPERGÉO- MÉTRIQUE
N D
N n
N
...
, 2 , 1
...
, 1
...
, 2 , 1
=
=
= 0,1,...,n
−
−
n N
x n
D N x D
N n D
N
nD
− N
1 D
−
− 1 N
n N
POISSON λ>0 0,1,2,...
)
! exp( λ
λ −
x
x λ λ
CONTINUES
UNIFORME αα ββ
<
,
[
α, β]
α β−
1
2 β α +
12 ) (β −α 2
EXPONEN-
TIELLE λ>0
[ )
0,∞ λ exp(−λx)λ 1
2
1 λ
GAMMA 0
0
>
>
λ
r
[ )
0,∞) ) exp(
(
1 x
r x
r r
λ −λ
Γ
− λ
r
λ2
r
WEIBULL 0
0
>
>
β
α
[ )
0,∞
−
− β
β
β α
α x x
exp 1
1 1
+
Γ β
α 1 1
+ Γ
−
+ Γ
β α β
1 1 1 2
2 2
___________________________________________________________________________________
Bernard Clément, PhD 2003
D I S T R I B U T I O N S ( suite )
Nom Paramètres Domaine Masse / Densité Moyenne Variance
CONTINUES
GAUS- SIENNE N (µ,σ2)
>0
∞
<
<
∞
−
σ µ (−∞,∞)
− −
2
2 exp 1 2 1
σ µ π
σ
x µ σ2
LOG NOR- MALE LN (ε,τ2)
>0
∞
<
<
∞
−
τ ε
[ )
0,∞ ln 22 exp 1 1 2
1
−
− τ
ε π
τ
x
x
+ 2 2
exp µ 1σ exp
[
2ε+τ2] [
∗ eτ2 −1]
BETA
Be (α,β) 0 0
>
>
β
α
[ ]
0,1 1 1) 1 ) (
( ) (
)
( − − −
Γ Γ
+
Γ α β
β α
β
α x x
β α
α
+ (α β)2(1 α β)
β α
+ + +
KHI-DEUX Xν2
...
, 2 ,
=1
ν
[ )
0,∞ exp[ 2)) 2 ( 2
1 2 1
2 x −x
Γ
ν −
ν ν ν 2 ν
STUDENT Tυ
...
, 2 ,
=1
ν (−∞,∞)
Γ
Γ +
2 2
1
πν ν ν
2
2 1
1
− +
+
ν
ν
x 0
) 2 2 ( >
− ν
ν ν
FISHER F
ν1,ν2 1,2,...
...
, 2 , 1
2 1 =
= ν
ν
[ )
0,∞2 , 1ν
cν
2 2
1 1 2 1
2 1
1
ν ν ν
ν
ν +
−
+ x
x
2
2
ν − ν
) 4 ( ) 2 (
) 2 (
2
2 2 2 1
2 1 2 2
−
−
− ν ν
ν
ν ν ν
2 2 1 2 1
2 1 2
, 1
1
2 2
2
ν ν
ν ν
ν ν ν
ν ν
Γ
Γ
+
Γ
= c
