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Monte Carlo Analysis
Additional Uncertainty Analyses (the .mcm File)
Additional Uncertainty Analyses (the .mcm File)
The .mcm file contains additional numerical summaries of the statistical tests.
Basic Concepts on Quantitative Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491
Robust Measures of Location . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492
Alternative Measures of Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494
Min/Max Values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495
Parametric Fit and Normality Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495
Capability Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499
Coorelation of Test Concordance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 500
Monte Carlo Sensitivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501
Basic Concepts on Quantitative Statistics
In statistics, it is very common to use in a complementary way, graphical techniques and
quantitative techniques. For example, if the quantitative methods yield different conclusions
than the graphical analysis, then some effort should be invested to understand why. Often this is
an indication that some of the assumptions of the classical techniques are not satisfied. Many of
the quantitative techniques given in the .mcm file fall into two general categories:
• Interval estimates
• Hypothesis tests
Interval Estimates
A classical task in statistics is to estimate a parameter from a sample of data. The value of the
parameter using all of the possible data, not just the sample data, is called the population
parameter or true value of the parameter. An estimate of the true parameter value is made using
the sample data. This is called a point estimate or a sample estimate.
For example, the most commonly used measure of centrality or location is the mean. The
population mean (or the “true” mean) is the sum of all the members of the given population
divided by the number of members in the population. In our simulation context, random
variables have continuous distributions, it is therefore impossible to simulate every member of
the population. A random sample is drawn from the population with the Monte Carlo method.
The sample mean is calculated by summing the values in the sample and dividing by the number
of values in the sample. This sample mean is then used as the point estimate of the population
mean.
Interval estimates incorporate the uncertainty of the point estimate. In the example for the mean
above, different samples from the same population will generate different values for the sample
mean (for example by varying the seed value in the .MC command setup). An interval estimate
Eldo® User's Manual, 15.3 491