Titel_SS06

min

(^22) min 2

1

()(1)

2

()(1)(1)

T

T

X

X

u

k

u

kk

' '

'

  +

 + + 

(^89) 

1

(2.83)

Distribution type Parameters Moments

Extreme Type I

Gumbel max

         x

fX( )xxuxu 55 exp( ( ) exp( 5 ( )))

FxX( )exp( exp( 5 (xu)))

0

u

a&

 u 0.577216

5



6





5



Extreme Type I

Gumbel min

         x

fX( )xxuxu 55 exp( ( ) exp( ( 5 )))

FxX( ) 1 exp( exp( (  5 xu)))

0

u

a&

 u 0.577216

5



6

 

5



Extreme Type II

Frechet max

' xuk, , & 0

1

() exp

kk

X

fx ku u

ux x

''

'' '

(^)!
! !
"# "#"#"#
$% $%$%
() exp
k
X
Fx u
x

'

'

! !

"#"#"

$%$%

0

0

u

k

'

&

&^

1

()1 , 1uk

k

'  + ' !"#&

$%

2

()

11,^21

u

k

kk

2

'

+ + ! !&

"#"

$%$%

Extreme Type III

Weibull min

' xuk, , & 0

1

() exp

kk

X

kx x

fx

uu u

''

'' '

 !

!!

"# "#"#"

$% $%$%



() 1 exp

k

X

x

Fx

u

'

'

! !

 "#"#"

$%$%

0

0

u

k

'

&

&

1

()1u

k

'  + ' !"

$%

()1u^2121

kk

' + +! !"#"

$%$%

Table 2.8: Probability distributions, Schneider 1994.