EM 1110-2-1100 (Part II)
30 Apr 02
Distribution
Mathematical
Mean & Standard Deviation
Parameters
Function
x ' B % 0.5772A
A ' 0.779 σx
Fisher-Tippett
x&B
&
A
F(x) ' e &e
σ ' 1.283A
I (FT-I)
B ' x & 0.4500 σx
or Gumbel
1
x'B%AΓ 1%
k
k
x&B
&
A
F(x) ' 1 & e
2
1
& Γ2 1 %
σx ' A Γ 1 %
general
k
k
Weibull
A ' 0.621 σx
k ' 0.75
x ' B % 1.191 A
σx ' 1.611 A
B ' x & 0.740 σx
k ' 1.0
x'B%A
A ' σx
σx ' A
B ' x & σx
k ' 1.4
x ' B % 0.911 A
A ' 1.515 σx
σx ' 0.660 A
B ' x & 1.380 σx
k ' 2.0
x ' B % 0.886 A
A ' 2.160 σx
σx ' 0.463 A
B ' x & 1.914 σx
&k
x
&
A
F(x) ' e
general
1
x'AΓ 1&
k
k ' 2.5
Fisher-Tippett
k ' 3.3
II (FT-II) or
2
1
& Γ2 1 &
σx ' A Γ 1 &
Frechet
k
k
k ' 5.0
k ' 10.0
Figure II-8-2.
Probability distribution functions for long-term statistics - Part 1 (Continued)
Hydrodynamic Analysis and Design Conditions
II-8-7
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