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• MCCORR(LABEL_EXT1,LABEL_EXT2)<br />

Monte Carlo Analysis<br />

Output of Uncertainty Analysis (the .chi File)<br />

Returns the pairwise-linear correlation coefficient between each pair of output measures.<br />

The sample correlation coefficient between two random variables (U, V) is given by the<br />

formula:<br />

(see the section Coorelation of Test Concordance for more information).<br />

• MCCOVAR(LABEL_EXT1,LABEL_EXT2)<br />

Returns the pairwise-linear covariance coefficient between each pair of output measures.<br />

The sample covariance coefficient between two random variables (U, V) is given by the<br />

formula:<br />

When the value U i or V i is undefined, because the corresponding extract function cannot<br />

be measured at the i-th run of the Monte Carlo simulation, then this data is removed<br />

from the computation. When all the pairwise data are removed, Eldo will return the<br />

value UNDEF (see the section Coorelation of Test Concordance for more information).<br />

• MCPROB(LABEL_EXT,LE | GE, BOUND_VALUE)<br />

Returns the probability π y that a given response is less or greater than a <strong>user</strong>-defined<br />

bound y. We write this probability as follows:<br />

when the second argument is LE, or<br />

when the argument is GE. The probability can be recast into the evaluation of the<br />

expectation<br />

where I {A} is the indicator function of the event A, and<br />

therefore computed through Monte Carlo simulations as follows:<br />

Eldo® User's Manual, 15.3 467

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