#' Calculate the error in matching a specified confidence interval with a Gamma distribution prior.
#'
#' @param shape The shape ("gamma") parameter of a Gamma distribution
#' @param lower_CI The lower confidence limit that we are trying to match
#' @param upper_CI The upper confidence limit that we are trying to match
#' @param mean The mean of the Gamma distribution (= shape * scale)
#' @param confidence_level The confidence level of the confidence interval (1 - alpha)
#' @param alpha = 1 - `confidence_level`
#' @return The sum of relative squared errors between the confidence limits and the quantiles of the fitted distribution.
#' @importFrom stats qgamma
sum_squares = function(
shape,
lower_CI,
upper_CI,
mean,
confidence_level = .95,
alpha =
(1-confidence_level)/2)
{
lower_quantile =
stats::qgamma(
shape = shape,
scale = mean/shape,
p = alpha,
lower = TRUE)
upper_quantile =
stats::qgamma(
shape = shape,
scale = mean/shape,
p = alpha,
lower = FALSE)
SS =
(lower_quantile - lower_CI)^2/lower_CI^2 +
(upper_quantile - upper_CI)^2/upper_CI^2
return(SS)
}
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