Evaluating reliability in geotechnical engineering - Risk and Reliability in Geotechnical Engineering - page 138

0.25

0.20

0.2

Lognormal distribution
(z= 0.147 (Std dev. = 2 kPa
Right scale

0.15

0.15

Average s u = 14 kPa
Std dev. = 2 kPa

0.10

0.1

0.05

0.05

0 0.00

0 5 10 15 20 25 30

s u (kPa)

Figure 3.5 Relative frequency diagram of measured undrained shear strength data with superimposed
lognormal probability distribution.

0.25 0.25

Average s u = 14 kPa
Standard deviation = 2 kPa

0.2 0.20

Normal distribution right scale

0.15 0.15

0.1 0.10

0.05 0.05

0 0.00

0 5 10 15 20 25 30

s u (kPa)

Figure 3.6 Relative frequency diagram of measured undrained shear strength data with superimposed
normal probability distribution.

theoretical distributions, it appears that the normal distribution in Figure 3.6 is a closer it
than the lognormal distribution in Figure 3.5 , by a small margin.

3.3.10 Cumulative density function
CDF is the integral of the PDF, that is, it is the area under the PDF curve, computed from
minus infinity to the value shown on the horizontal axis. The value of the CDF for any value