Titel_SS06

: 1 4.04

: 2 32.665

Not surprisingly the same result as the method of moments.

As mentioned previously the covariance matrix for the parameters estimates may be
determined through the Fischer information matrix H containing the second-order partial
derivatives of the log-likelihood function, see Equation

C

(2.101). The information matrix may
be found to be:

 





2

22

11

24 3

11 1

2

1

32

11

3- 2-

2-

nn

ii

ii

n

i

i

xx

n

x

n

::

:: :

:

::





!

"

"#

"

"

"

"

"#$%





H

!

(2.104)

whereby the covariance matrix is evaluated using the sample data as:

1 0.836^0

0 0.1647

^

"

$%

CH (2.105)

In a probabilistic modelling where the concrete cube compressive strength enters as a random
variable it is then possible to take into account the statistical uncertainty associated with the
estimates of the distribution parameters for the distribution function simply by including the
distribution parameters in the reliability analysis as Normal distributed variables with the
evaluated mean values and covariances.