R/axMidpoint.R

In MortHump: Measure the Young Adult Mortality Hump

#' @title axMidpoint approximates a(x) using interval midpoints
#'
#' @description approximates a(x) using interval midpoints (except a0, which is estimated using a rule-of-thumb formula scaled by m0)
#'
#' @param Mx a numeric vector of central death rates, defined as deaths/exposure.
#' @param n a numeric vector of the age-interval widths. Must be the same length as Mx.
#'
#' @details All values will be in the exact middle of the age interval, except for a0, which uses: \code{a0 = .07 + 1.7 * M0}.
#'
#' @return returns a numeric vector of ax values
#'
#' @references formula for a0 as suggested by:
#' Keyfitz, N. (1970), Finding probabilities from observed rates, or how to make a life table. The American Statistician (1970), pp. 28-33
#'
#' @seealso See Also \code{\link{axEstimate}}, a wrapper function for this and 3 other a(x) estimation methods (\code{\link{axKeyfitz}},\code{\link{axSchoen}} and \code{\link{axPreston}}).
#'
#' @author Tim Riffe
#'
#' @export

axMidpoint <-
function(Mx, n){
	ax      <- .5 * n
	ax[1]   <- .07 + 1.7 * Mx[1] # I guess this is Keyfitz + Flieger?
	return(ax)
}