#' Confidence Interval - Theta Hit
#'
#' @author Ivan Jacob Agaloos Pesigan
#' @family confidence intervals functions
#' @keywords ci
#' @param lo Numeric.
#' Lower limit of the estimated confidence interval
#' \eqn{\left( \hat{\theta}_{\mathrm{lo}} \right)}.
#' @param theta Numeric.
#' Population parameter
#' \eqn{\left( \theta \right)}.
#' @param up Numeric.
#' Upper limit of the estimated confidence interval
#' \eqn{\left( \hat{\theta}_{\mathrm{up}} \right)}.
#' @return Returns
#' `TRUE` if `theta` \eqn{\left( \theta \right)} is between the interval
#' `lo`
#' \eqn{\left( \hat{\theta}_{\mathrm{lo}} \right)}
#' to
#' `up`
#' \eqn{\left( \hat{\theta}_{\mathrm{up}} \right)}.
#' Returns
#' `FALSE` if `theta` \eqn{\left( \theta \right)} is outside the interval
#' `lo`
#' \eqn{\left( \hat{\theta}_{\mathrm{lo}} \right)}
#' to
#' `up`
#' \eqn{\left( \hat{\theta}_{\mathrm{up}} \right)}.
#' @examples
#' # FALSE
#' theta_hit(lo = 1, theta = 0, up = 2)
#' # TRUE
#' theta_hit(lo = -1, theta = 0, up = 1)
#' @export
theta_hit <- function(lo,
theta,
up) {
lo < theta & theta < up
}
#' Confidence Interval - Zero Hit
#'
#' @author Ivan Jacob Agaloos Pesigan
#' @family confidence intervals functions
#' @keywords ci
#' @inheritParams theta_hit
#' @return Returns
#' `TRUE` if zero is between the interval
#' `lo`
#' \eqn{\left( \hat{\theta}_{\mathrm{lo}} \right)}
#' to
#' `up`
#' \eqn{\left( \hat{\theta}_{\mathrm{up}} \right)}.
#' Returns
#' `FALSE` if zero is outside the interval
#' `lo`
#' \eqn{\left( \hat{\theta}_{\mathrm{lo}} \right)}
#' to
#' `up`
#' \eqn{\left( \hat{\theta}_{\mathrm{up}} \right)}.
#' @examples
#' # FALSE
#' zero_hit(lo = 1, up = 2)
#' # TRUE
#' zero_hit(lo = -1, up = 1)
#' @export
zero_hit <- function(lo,
up) {
theta_hit(
lo,
theta = 0,
up
)
}
#' Confidence Interval - Length
#'
#' Calculates confidence interval length.
#'
#' The confidence interval length is given by
#' \deqn{
#' \mathrm{
#' confidence \ interval \ length
#' }
#' =
#' \hat{
#' \theta
#' }_{
#' \mathrm{
#' up
#' }
#' }
#' -
#' \hat{
#' \theta
#' }_{
#' \mathrm{
#' lo
#' }
#' }
#' }
#'
#' @author Ivan Jacob Agaloos Pesigan
#' @family confidence intervals functions
#' @keywords ci
#' @inheritParams theta_hit
#' @export
len <- function(lo,
up) {
up - lo
}
#' Confidence Interval - Shape
#'
#' Calculates confidence interval shape.
#'
#' The confidence interval shape is given by
#' \deqn{
#' \mathrm{
#' confidence \ interval \ shape
#' }
#' =
#' \frac{
#' \hat{
#' \theta
#' }_{
#' \mathrm{
#' up
#' }
#' }
#' -
#' \hat{
#' \theta
#' }
#' }
#' {
#' \hat{
#' \theta
#' }
#' -
#' \hat{
#' \theta
#' }_{
#' \mathrm{
#' lo
#' }
#' }
#' }
#' }
#'
#' The shape measures the asymmetry of the confidence interval
#' around the point estimate
#' \eqn{
#' \hat{
#' \theta
#' }
#' }.
#' Shape
#' \eqn{
#' >
#' 1.00
#' }
#' is indicative of greater distance between
#' \eqn{
#' \hat{
#' \theta
#' }_{
#' \mathrm{
#' up
#' }
#' }
#' }
#' and
#' \eqn{
#' \hat{
#' \theta
#' }
#' }
#' than
#' \eqn{
#' \hat{
#' \theta
#' }
#' }
#' and
#' \eqn{
#' \hat{
#' \theta
#' }_{
#' \mathrm{
#' lo
#' }
#' }
#' } .
#'
#' @author Ivan Jacob Agaloos Pesigan
#' @family confidence intervals functions
#' @keywords ci
#' @inheritParams theta_hit
#' @param thetahat Numeric.
#' Parameter estimate
#' \eqn{
#' \left(
#' \hat{
#' \theta
#' }
#' \right)
#' } .
#' @export
shape <- function(lo,
thetahat,
up) {
(up - thetahat) / (thetahat - lo)
}
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