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diff --git a/R/sigma_twocomp.R b/R/sigma_twocomp.R index b06816c1..c9a15aa8 100644 --- a/R/sigma_twocomp.R +++ b/R/sigma_twocomp.R @@ -1,3 +1,29 @@ +#' Two component error model +#' +#' Function describing the standard deviation of the measurement error in +#' dependence of the measured value \eqn{y}: +#' +#' \deqn{\sigma = \sqrt{ \sigma_{low}^2 + y^2 * {rsd}_{high}^2}} sigma = +#' sqrt(sigma_low^2 + y^2 * rsd_high^2) +#' +#' This is the error model used for example by Werner et al. (1978). The model +#' proposed by Rocke and Lorenzato (1995) can be written in this form as well, +#' but assumes approximate lognormal distribution of errors for high values of +#' y. +#' +#' @param y The magnitude of the observed value +#' @param sigma_low The asymptotic minimum of the standard deviation for low +#' observed values +#' @param rsd_high The coefficient describing the increase of the standard +#' deviation with the magnitude of the observed value +#' @return The standard deviation of the response variable. +#' @references Werner, Mario, Brooks, Samuel H., and Knott, Lancaster B. (1978) +#' Additive, Multiplicative, and Mixed Analytical Errors. Clinical Chemistry +#' 24(11), 1895-1898. +#' +#' Rocke, David M. and Lorenzato, Stefan (1995) A two-component model for +#' measurement error in analytical chemistry. Technometrics 37(2), 176-184. +#' @export sigma_twocomp <- function(y, sigma_low, rsd_high) { sqrt(sigma_low^2 + y^2 * rsd_high^2) } |