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probabilistic Design analysis • 81
0.4
0.35
0.3
0.25
Probability 0.15
0.2
0.1
0.05
0
-6 -4 -2 0 2 4 6
X
Power normal distribution
0.7
0.6
0.5
Probability 0.4
0.3
0.2
0.1
0
0 2 4 6 8 10 12
x
Power lognormal distribution
3.2.2 noRMAL DiSTRibUTion
3.2.2.1 Probability Density Function
The general formula for the probability density function of the normal
distribution is:
x (
e −− ) m 2 / ( )
s
2
2
fx () =
s 2 p
where m is the location parameter and is the scale parameter.
The case where m = 0 and s = 1 is called the standard normal
distribution. The equation for the standard normal distribution is:
