Evaluates, at the statistic values t, the global-null CDF
\(F_{00}(t) = \int_0^1 G_t(q)dq\), its empirical counterpart
\(\hat Q(t) = J^{-1}\sum_j G_t(p_{de,j})\), the reconstructed
\(\hat F_{01}(t) = \{\hat Q(t) - \hat\pi_{00}F_{00}(t)\}/(\hat\pi_{01}+\hat\pi_{11})\)
(truncated to [0, 1] and made nondecreasing in \(t\) by a running maximum;
set to 0 if \(\hat\pi_{01}+\hat\pi_{11} = 0\)), the null numerator
\(\hat N(t) = \hat\pi_{00}F_{00}(t) + \hat\pi_{01}\hat F_{01}(t)\) and the
composite null CDF \(\hat F_0(t) = \hat N(t) / (\hat\pi_{00} + \hat\pi_{01})\),
where \(G_t(q) = \min\{1, (t/(\kappa_1 q^{1-\alpha_2} + \kappa_2))^{1/(1-\alpha_1)}\}\).
Arguments
- log_t
Values of \(\log t\).
- p_de
All decorrelated p-values (used for \(\hat Q\)).
- par
Parameter list as in
heart_statistic(), also containingpi11(orpi10, from which \(\pi_{11} = 1 - \pi_{00} - \pi_{01} - \pi_{10}\)).- exact
If
FALSE, \(F_{00}\) is computed exactly at then_exactsmallest values and interpolated (log-log) on ann_gridgrid elsewhere.- n_exact, n_grid
See
exact.