eldo_user

Monte Carlo Analysis
Primary Statistics of Uncertainty Analysis
This should result in a good estimate if the model m(x) is a good approximation of H(x), but the
main issue lies in quantifying the uncertainty in the estimate. One consider estimates of the
distribution function based on extreme estimates of H(x)
where c(Xi) is a measure of variance at the point Xi coming from a 100(1−α)% prediction
interval for an unknown observation. It is important to note that there is no theoretical
justification for this expression. These “pseudo-bounds” are only related to the quantities that
we are interested in. The previous expression is based on the distribution function for
100(1-α)% pointwise bounds on H(X), when the real interest is in pointwise bounds of the
distribution function of H(X).
How to Interpolate the CDF function
We provide the order statistics in the .mco file and the associated uniformly spaced cumulative
probabilities: (Y (i) , p i ). These values can be useful to work with a piecewise linear
approximation of the cumulative distribution. We describe how you can build a continuous
approximation of the CDF and how the confidence intervals are defined point-wise on this
function.
If Y (1) , Y (2) , …, Y (n) is the sample sorted from smallest value to largest value. The order statistics
Y (i) can be found in the column labelled with “Value(order)” and the cumulative probabilities in
the column “CDF(Cum.Prob)”:
.
. ==> Main sample (runs 1..1000)
.
.
.
. Index Output Measure 1 : MAX
. of Run/ Index
. Order of Meas ... Value(order) CDF(Cum.Prob) +/- T*STD
. -------------------------------------------------------------------------------
1 1 ... 7.1261259e-01 1.0000000e-03 6.1992631e-05
2 1 ... 7.1281508e-01 2.0000000e-03 1.2386115e-04
3 1 ... 7.2847591e-01 3.0000000e-03 1.8560556e-04
4 1 ... 7.3749211e-01 4.0000000e-03 2.4722587e-04
5 1 ... 7.3848200e-01 5.0000000e-03 3.0872206e-04
6 1 ... 7.3881086e-01 6.0000000e-03 3.7009415e-04
7 1 ... 7.3981639e-01 7.0000000e-03 4.3134212e-04
...
To build the function
we define:
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Eldo® User's Manual, 15.3