EM 1110-2-1100 (Part II)
30 Apr 02
Distribution
Mathematical Expression
Mean & Standard
Parameters
Function
Deviation
1 2
A
B%
2
2
lnx & B
x'e
&
1
A
e
f(x) '
Log-Normal
Ax π
2
2
σx ' e (2 B % A )(e A & 1)
k ' skew of ln x corrected
for bias
lnx ' B % Ak
lnx&B
k&1
σ
&
1
lnx&B
Log Pearson
A
f(x) '
e
A ' lnx
A x Γ (k)
A
Type III
k
σl n x ' A k
(Kite 1978)
B ' l n x & σl n x k
2 2
k'
G
x ' B % Ak
x&B
k&1
&
1
x&B
G ' skew coefficient
A
f(x) '
e
A Γ (k)
A
σ
Pearson
A' x
σx ' A k
Type III
k
B ' x & σx k
N!
x'Np
px 1 & p
N&x
f(x) '
Binomial
x! N & x !
(discrete)
σx ' N p (1 & p)
x'λ
λx e & λ
f(x) '
Poisson
σx ' λ
x!
(discrete)
Figure II-8-2.
Probability distribution functions for long-term statistics - Part 2 (concluded)
II-8-8
Hydrodynamic Analysis and Design Conditions
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