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Approximations of the CDF
Monte Carlo Analysis
Primary Statistics of Uncertainty Analysis
Recall that the Monte Carlo method enables the computation of the full empirical CDF function
of the random output Y=H(X).
We will first explain how the distribution function is built for the standard Monte Carlo
method and secondly for the model-based approach. The second section is devoted to the
presentation of these results and how to use it.
CDF Function and Confidence Bounds
The computation of the empirical CDF uses the simulated sample Y 1 , …, Y n and is given by a
staircase function whose usual definition resembles the Monte Carlo estimator in:
This function approximates the probability
follows:
. Its estimated variance is defined as
This variance in turns enables an approximation of the 100(1−α)% confidence interval bounds
on the empirical CDF thanks to the Central Limit Theorem (provided the number of runs n is
sufficiently large). These two bounds read as follows:
where
is an appropriate percentage point from the normal distribution.
In the case of model-based approach, one proposes to consider estimating
substitution:
by simple
Eldo® User's Manual, 15.3 485