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Chapter 3. The randvar class
Name
21
f (x)
”Normale”
2σ
(
”Uniforme”
1
√
exp
2π
1
b−a ,
0
2
− 12 (x−µ)
σ2
if x ∈ [a, b[
if x ∈
/ [a, b[
E(X)
V (X)
µ
σ2
b+a
2
(b−a)2
12
1
λ
1
λ2
(
”Exponentielle”
”LogNormale”
λ exp (−λx) , if x > 0
0
if x ≤ 0
(
2
1 (ln(x)−µ)
1
√
exp
−
,
2
2
σ
σx 2π
if x ≤ 0
0
(
”LogUniforme”
if x > 0
1
1
x ln(b)−ln(a) ,
if x ∈ [a, b[
0
if x ∈
/ [a, b[
exp µ + 12 σ 2
b−a
ln(b)−ln(a)
exp(σ 2 ) − 1 exp 2µ + σ 2
1
b2 −a2
2 ln(b)−ln(a)
− E(x)
Fig. 3.1 : Distributions functions of the ”randvar” class. – The expected value is denoted by E(X) and
the variance is denoted by V (X).
Name
”Normale”
”Uniforme”
”Exponentielle”
”LogNormale”
”LogUniforme”
Parameter #1 : a Parameter #2 : b
µ = 0.
σ = 1.
a = 0.
b = 1.
λ = 1.
µ0 = 0.1
σ = 1.0
a = 0.1
b = 1.0
Conditions
σ>0
a<b
µ0 , σ > 0
a, b > 0, a < b
Fig. 3.2 : Default parameters for distributions functions.