Page 459 - Marine Structural Design

Chapter 24 Random Variables and Uncertainty Analysis 435

for -colxla~ (24.7)

where s=(x-px)/a. When ,UFO, a,l, the normal distribution is called Standard Normal
Distribution.
Lognormal Distribution
The probability density function and its cumulative distribution function for the lognormal
distribution are defined by

(24.8)

for x20 (24.9)

where the mean value and standard deviation are given by

(24.10)

(24.1 1)

Rayleigh Distribution
ex.[ - -(-I]
The Rayleigh distribution is defined by

p(x) = a2 2 1 x-u for x2u (24.12)
a
Fx (x) = 1 - exp[ - ;(?I] for x2u (24.13)

where
ZA = location parameter
a = scale parameter
The mean value and standard deviation are given by

(24.14)

ax =adT 4--7c
(24.1 5)