Titel_SS06

The relevance of the different distribution functions given in Table 2.7 in connection with the
probabilistic modelling of uncertainties in engineering risk and reliability analysis is strongly
case dependent and the reader is suggested to consult the application specific literature for
specific guidance. In the following a few specific remarks will, however, be provided for the
commonly applied Normal distribution and the Lognormal distribution.

Distribution type Parameters Moments

Uniform, axb

()^1

fxX ba

FxX() x a

ba

 



a

b

2

ab^

12

ba

Normal

112

() exp

X 2 2

x

fx



 

! !

"#"#"

$%$%

112

() exp

2 2

x

X

t

Fx dt



 

! !

"#"#"

 $%$%



& 0





Shifted Lognormal, x&'

2

11ln()

() exp

X ()2 2

x

fx

x

'(

')  )

! !

"" "

 $ $%%

ln( )

X() 

x

Fx

'(

)

!

 "

$%

(

)> 0

'

2

exp

2

)

' (

!

 "

$%

(^22)
exp exp( ) 1
2

)

( )

!

 "# 

$%

Shifted Exponential, x*'

fxX( )(('exp( (x))

FxX() 1 exp  

('

x

'

(& 0

'^1

(



^1

(



Gamma, x* 0

() exp( )^1

()

p

p

X

b

f xb

p



+

xx

,

()

X ()

bx p

Fx

p

+



+

p& 0

b& 0

p

b



p

b