140
10 Defining Probabilities of Events
0
1
2
3
4
5
6
7
8
9
1 0
1 1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Number of Events
Probability
Fig. 10.1 With a measured frequency of 1.5 events/year the probability of occurrence (vertical
axis) of 1, 2, 3, … n events next year (horizontal axis) can be evaluated using Poisson’s distribution
For small frequencies (up to 1/10 years (units)), one can assume annual probability
≈ frequency, as shown in Fig. 10.2. However, at frequency = 1/5 years (f = 0.2) the
error of the approximation rises to 20%. After that, you need Poisson’s distribution.
The probability of an event occurring once or more within its return period is
always 0.63. This is because the likelihood of seeing no event within its return
period is 0.37, which is e
−1 .
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
0.1
1
10
100
1000
Frequency
Probability
Fig. 10.2 Frequency versus probability plot. The vertical axis shows probabilities (bound to one),
the horizontal axes bears frequencies
10 Defining Probabilities of Events
0
1
2
3
4
5
6
7
8
9
1 0
1 1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Number of Events
Probability
Fig. 10.1 With a measured frequency of 1.5 events/year the probability of occurrence (vertical
axis) of 1, 2, 3, … n events next year (horizontal axis) can be evaluated using Poisson’s distribution
For small frequencies (up to 1/10 years (units)), one can assume annual probability
≈ frequency, as shown in Fig. 10.2. However, at frequency = 1/5 years (f = 0.2) the
error of the approximation rises to 20%. After that, you need Poisson’s distribution.
The probability of an event occurring once or more within its return period is
always 0.63. This is because the likelihood of seeing no event within its return
period is 0.37, which is e
−1 .
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
0.1
1
10
100
1000
Frequency
Probability
Fig. 10.2 Frequency versus probability plot. The vertical axis shows probabilities (bound to one),
the horizontal axes bears frequencies