eldo_user

Monte Carlo Analysis
How to Specify a Distribution Function
The probability density function is expressed as:
where φ and Φ represent the probability density and the cumulative distribution function
respectively of the reduced centred Normal distribution (that is, the mean μ zero and standard
deviation σ equal to 1).
A random variable that follows a truncated Normal distribution takes values in the interval
[a, b]. The parameter μ describes the most likely value. Whilst σ provides a measure of
dispersion. Figure 11-6 shows an example with μ = 20, σ = 7, and [a, b] = [10, 35].
In Eldo, the centered and reduced Gaussian variables are generated with the truncated normal
distribution before transformation to the original scales of the input space.
Figure 11-6. Plot of the Truncated Normal
The bounds of the truncation interval are fixed by default to the SIGTAIL value. Note that this
interval is necessarily a symmetric interval.
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Eldo® User's Manual, 15.3