#' Derivative of objective function to be minimized, as described by...
#'
#' @param w weight corresponding to theta; i.e., w(theta)
#' @param theta the mean of sampling distribution y
#' @param sigma standard deviation of sampling distribution for y
#' @param t the truncation, i.e. y ~ N(theta, sigma) * 1(abs(y) > t)
#' @param alpha confidence level
#' @param marginal_fun the function for the marginal distribution
#' @param ... optional arguments to the marginal function
#'
#' @export
Hprime_w_safab1 <- function(w, theta, sigma, t, alpha, marginal_fun, ...) {
F_inv_1 <- qtnorm1(alpha * w + 1 - alpha, theta, sigma, t)
F_inv_2 <- qtnorm1(alpha * w , theta, sigma, t)
marginal_fun(F_inv_1, sigma = sigma, t = t, ...) /
dtnorm1(F_inv_1, theta, sigma, t) -
marginal_fun(F_inv_2, sigma = sigma, t = t, ...) /
dtnorm1(F_inv_2, theta, sigma, t)
}
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