Measures sensitive to number of exceedence

Performance measures 1, 2 and 3 are digital measures sensitive to the concept of exceedence as defined by the event set $\Phi$ (expression ) and are entirely based on the cardinality of these or similar ($\Psi$ for measure 3) sets as a function of confidence level c. As already remarked (in the detailed specification) - these measures are oblivious to the degree of exceedence - and hence lacking in this respect. It is quite possible that two models may have the same number of exceedences - even at the same points in time - but one model barely overshoots the exceedence limit $\chi(c)$ whereas another goes well beyond. Clearly measures 1, 2 and 3 will be unable to discriminate between two such models.