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Gaussian or Normal Distribution
Monte Carlo Analysis
How to Specify a Distribution Function
In this case the parameters are Θ = (μ, σ), with the constraint σ > 0. The probability density is
given as:
We note that a random variable which follows a Gaussian distribution as defined here takes real
values from (−∞, ∞). The simulated values are actually truncated to some user-defined interval.
This interval is defined with the SIGTAIL argument on the .MC statement. See the Remarks on
the Truncated Normal Distribution.
The parameter μ provides the most likely value (for which the probability density function is at
its highest), and the density function is symmetric around this value; μ is also the expected value
(mean) of this distribution. The parameter σ provides a measure of dispersion: the larger it is,
the flatter the probability density function is (that is, values far away from μ are still likely, or in
other words possible values are more spread out).
The plot in Figure 11-5 depicts the common statistics of the Gaussian distribution.
Figure 11-5. Percentage of Cases in Eight Portions of the Gaussian Distribution
This plot may help you define the SIGTAIL argument of the .MC analysis. For example, the
range [−σ, σ] represents 34.13% + 34.13% = 68.26% of cases obtained after running the sample
process in the Monte Carlo algorithm, and the range [−3σ, 3σ] covers 2(34.13% + 13.59% +
2.14%) = 99.72% of the cases.
Remarks on the Truncated Normal Distribution
For the truncated Normal distribution, the parameters are Θ = (μ, σ, a, b), with the constraints
that σ > 0, b > a.
Eldo® User's Manual, 15.3 433