Check if the argument is a scalar within specified range
Check if the argument is within specified range
Check if the argument is a scalar integer within specified range
Check if the argument is an integer vector within specified range
The computation involves a \(J-1\) multivariate normal integral of the conditional density of the \(i\)-th subgroup statistic given that it was maximal among all subgroups:
scalarInRange(x, low = -Inf, high = Inf)numberInRange(x, low = -Inf, high = Inf)
scalarIntegerInRange(x, low = -Inf, high = Inf)
integerInRange(x, low = -Inf, high = Inf)
den.vs(v, i, mu.prime, Sigma.prime, fut)
TRUE or FALSE
TRUE or FALSE
TRUE or FALSE
TRUE or FALSE
the conditional probability
the lower bound, default -Inf
the upper bound, default Inf
the value of the statistic
the subgroup
the conditional mean vector of the distribution of
length \(J - 1\); needs to be multipled by the conditional
value, the parameter v.
the conditional covariance matrix of dimension \(J-1\) by \(J-1\)
the futility boundary, which is \(\tilde{b}\) for stages 1 and 2, but \(c\) for stage 3
$$ \phi_i(v)(\int_0^v\int_0^v\ldots \int_0^{\tilde{b}} \phi_v(z_{-i})dz_{-i}) $$
where \(z_{-i}\) denotes all subgroups other than \(i\).