Kupiec test, Christoffersen test क्या है?

The Kupiec test compares the number of exceptions $x$ in $n$ days with the expected $pn$ by the likelihood ratio $-2\ln[(1-p)^{n-x}p^x/((1-\hat p)^{n-x}\hat p^x)]$, $\hat p = x/n$, chi-square with one degree of freedom. The Christoffersen test checks independence: it compares the probability of an exception after an exception with the probability after a quiet day.