eldo_user

Monte Carlo Analysis
Additional Uncertainty Analyses (the .mcm File)
mean lacks robustness, that is confidence intervals based on the mean tend to be not precise if
the underlying distribution is in fact not normal.
The subsection “Robust Measures of Location” provides three of the classical robust measures
of location: the median, the mid-mean, and the trimmed-mean.
==> Robust Measures of Location:
Median ... Median Value (50th percentile)
Mid-Mean ... Mean between 25th and 75th percentiles
Trimmed Mean ... Mean with 5% of trimmed points in lower/upper tails
Index Nominal Mid Trimmed Name
of Meas Value Median Mean Mean of Meas
-----------------------------------------------------------------------------
1 8.38073e-01 8.37607e-01 8.37391e-01 8.37282e-01 MAX
2 2.19652e+00 2.19540e+00 2.19524e+00 2.19535e+00 BW
3 -5.44334e-02 -5.44314e-02 -5.44231e-02 -5.44296e-02 IVDD
What Robustness Means
There are two properties that we expect for robust measures of location, where robustness
means independence to the effects of non-normality:
• Robustness of type I: the confidence intervals for the population location have a large
probability of covering the population location regardless of what the underlying
distribution is.
• Robustness of type II: the confidence intervals for the population location tend to be
almost as narrow as the best that could be done if we knew the true shape of the
distribution.
The median is an example of an estimator that tends to have robustness of type I, but not of type
II. The median is the value of the point which has half the data smaller than that point and half
the data larger than that point. That is, if Y (1) , Y (2) , …, Y (n) is a sample sorted from smallest
value to largest value, then the median is defined as:
The alternative measures of location try to balance these two concepts of robustness. That is, the
confidence intervals for the case when the data are normal should be almost as narrow as the
confidence intervals based on the mean. However, they should maintain their validity even if
the underlying data are not normal.
Eldo® User's Manual, 15.3 493