Create an expected gpl loss function — exp_gpl_loss

This is the per-target contribution to the objective minimized by allocate().

Usage

exp_gpl_loss_fun(
  dg = function(u) 1,
  F,
  kappa = 1,
  alpha = NA,
  O = NA,
  U = NA,
  offset = 0
)

dg: derivative of the increment function g.
F: predictive cdf of the outcome.
kappa: scale factor.
alpha: normalized loss when the outcome y exceeds the allocation x. Exactly one of alpha and U must be supplied.
O: cost incurred when the allocation x exceeds the outcome y; equals kappa * (1 - alpha).
U: cost incurred when the outcome y exceeds the allocation x; equals kappa * alpha.
offset: a constant added to the expected loss. Unlike gpl_loss_fun(), a function-valued offset is not supported here, since its expectation would itself require integration.

A function of an allocation x giving the expected loss with respect to the distribution F.

Z <- exp_gpl_loss_fun(F = pnorm, alpha = 0.5)
Z(0)
#> [1] 0.3989423