The function sets up a 1 sample one-sided decision function with an arbitrary number of conditions which have all to be met.
oc1Sdecision(pc = 0.975, qc = 0, lower.tail = TRUE)vector of critical cumulative probabilities of the difference distribution.
vector of respective critical values of the difference
distribution. Must match the length of pc.
logical value selecting if the threshold is a lower or upper bound.
The function creates a one-sided decision function which
takes two arguments. The first argument is expected to be a mixture
(posterior) distribution. This distribution is tested whether it
fulfills all the required threshold conditions specified with the
pc and qc arguments and returns 1 of all conditions
are met and 0 otherwise. Hence, for lower.tail=TRUE
condition \(i\) is equivalent to
$$P(x \leq q_{c,i}) > p_{c,i}$$
and the decision function is implemented as indicator function on the basis of the heavy-side step function \(H\) which is \(0\) for \(x \leq 0\) and \(1\) for \(x > 0\). As all conditions must be met, the final indicator function returns
$$\Pi_i H_i(P(x \leq q_{c,i}) - p_{c,i} ).$$
When the second argument is set to TRUE a distance metric is
returned component wise as
$$ D_i = \log(P(p < q_{c,i})) - \log(p_{c,i}) .$$
These indicator functions can be used as input for 1-sample OC
calculations using oc1S.
oc1S