Page 96 - Using ANSYS for Finite Element Analysis Dynamic, Probabilistic, Design and Heat Transfer Analysis

probabilistic Design analysis • 83
• Many classical statistical tests are based on the assumption that the
data follow a normal distribution. This assumption should be tested
before applying these tests.
• In modeling applications, such as linear and nonlinear regression,
the error term is often assumed to follow a normal distribution with
fixed location and scale.
• The normal distribution is used to find significance levels in many
hypothesis tests and confidence intervals.

3.2.3 UniFoRM DiSTRibUTion

3.2.3.1 Probability Density Function

The general formula for the probability density function of the uniform
distribution is:
1
fx () = �� x ≤ B
forA ≤
B − A

where A is the location parameter and B - A is the scale parameter.
The case where A = 0 and B = 1 is called the standard uniform
distribution. The equation for the standard normal distribution is:

fx () = 1 for 0 ≤ x ≤ 1
Since the general form of probability functions can be expressed in
terms of the standard distribution, all subsequent formulas in this section
are given for the standard form of the function.
Figure 3.4 shows the uniform pdf.

2
1.8
1.6
1.4
Probability 0.8 1
1.2

0.6
0.4
0.2
0
0 1 2 3 4 5 6 7 8 9 10
X
Figure 3.4. The uniform probability density function.