# Rh/Fragment 111 04

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Expression (4.5.1) is a two-tailed test that is asymptotically distributed as binomial. We perform the null hypothesis that it is a method that correctly estimates the risk measures against the alternative that the method has a systematic estimation error and gives too few or too many violations. Under the null hypothesis that a method correctly estimates the conditional quantiles, the empirical version of the statistic ${\scriptstyle \sum_{t\in T} \mathbf{1}_{\{X_{t+1} > x^t_q\} } }$ is from the binomial distribution ${\scriptstyle B (card (T), 1-q) }$. We perform a two-sided binomial test of the null hypothesis against the alternative that the method has a systematic estimation error and gives too few or too many violations.