eldo_user

Monte Carlo Analysis
Primary Statistics of Uncertainty Analysis
The lower bound on the frequency FOSC is raised to increase the probability of simulating “tail
events”. The second probability estimator is kept at its original value. Running Eldo with
SAMPLING=RAND and 5000 runs produces a .mcm file containing the following data:
==> Table of Estimators and Confidence Intervals:
[...]
Tail Boundary/ Lower Pr. Value Upper CV(%) Name
Dist. Sigma Tail / Complementary of Meas
--------------------------------------------------------------------------------
Left 1.82000e+09 2.030e-01 2.144e-01/7.856e-01 2.258e-01 5.31% FOSC
-0.780 NQ = -0.831 -0.791 -0.753
WCI = 2.032e-01 2.146e-01/7.854e-01 2.260e-01 5.30%
Right -1.10000e+02 0.000e+00/1.000e+00 0.00% PHASE_N
19.736 ECI = 0.000e+00 5.991e-04
Note that the results differ for the two MCPROB functions:
• The results of the FOSC extract indicate that the left-tail probability is approximately
2.144×10 −1 , with confidence interval [2.030×10 −1 , 2.258×10 −1 ]. The precision or the
coefficient of variation is 5.3% at a 95% confidence level. This confidence interval is
known in the statistical literature as the Wald interval or the Normal approximation. The
formula is:
The line below the Wald interval contains the following information:
o
The value of q σ , which represents a normalized distance of the user specification
y = y l or y u . It is given by the following ratio:
In the case of perfect normality of the output Y, this value is the normal quantile of
the bound y. The value of q σ is -0.780 in the above example. Compare this value
with the NQ values contained in the same line.
o
The NQ values of the corresponding quantiles of the normal N(0, 1). If π y is a
probability given by the normal interval then the associated normal quantile is
y NQ = Φ −1 (π y ), where Φ is the distribution function of normal distribution N(0, 1).
The second NQ value in the above example is -0.791 ≈ Φ −1 (2.144×10 −1 ).
Eldo® User's Manual, 15.3 481