eldo_user

Monte Carlo Analysis
Additional Uncertainty Analyses (the .mcm File)
Alternative Measures of Location
These alternatives can solve the problem of heavy-tailed distributions:
• Mid-mean: computes a mean using the data between the 25th and 75th percentiles.
• Trimmed mean: similar to the mid-mean except different percentile values are used. A
common choice is to trim 5% of the points in both the lower and upper tails, that is,
calculate the mean for data between the 5th and 95th percentiles.
The first three alternative location estimators defined above have the advantage of the median in
the sense that they are not affected by extremes in the tails. However, they generate estimates
that are closer to the mean for data that are normal (or nearly so).
Alternative Measures of Dispersion
When analyzing the variability of a simulated sample, the designer may face two key questions:
• How spread out are the simulated values near the central value?
• How spread out are the tails?
In the normal case, the variance (and its square-root the standard deviation) fully answers to
these two points. But it is known that it lacks what we defined robustness of type I.
In the subsection “Alternative Measures of Dispersion” of the .mcm file, we provide the range
and the inter-quartile range. These two numerical summaries are different answers to these two
points. The choice of the dispersion estimator is often driven by which of these points you want
to summarize.
==> Alternative Measures of Dispersion:
IQR ... Inter-Quartile Range
Q1, Q3 ... Lower and Upper Quartile
Index Range IQR Name
of Meas [ Min , Max ] [ Q1 , Q3 ] of Meas
-------------------------------------------------------------------------
1 2.72468e-01 5.55356e-02 MAX
7.12613e-01 9.85080e-01 8.09695e-01 8.65231e-01
2 1.31492e-01 2.57794e-02 BW
2.13597e+00 2.26746e+00 2.18230e+00 2.20808e+00
3 4.67989e-03 1.02707e-03 IVDD
-5.68030e-02 -5.21231e-02 -5.49313e-02 -5.39042e-02
We define these summaries as follows:
• The range is the largest value minus the smallest value in a data set. This measure is
based only on the lowest and highest extreme values in the sample. The spread near the
center of the distribution is not captured at all.
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Eldo® User's Manual, 15.3