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-\name{lod}
-\alias{lod}
-\alias{lod.lm}
-\alias{lod.rlm}
-\alias{lod.default}
-\title{Estimate a limit of detection (LOD)}
-\usage{
-  lod(object, \dots, alpha = 0.05, beta = 0.05, method = "default")
-}
-\arguments{
-  \item{object}{
-    A univariate model object of class \code{\link{lm}} or 
-    \code{\link[MASS:rlm]{rlm}} 
-    with model formula \code{y ~ x} or \code{y ~ x - 1}, 
-    optionally from a weighted regression.
-  }
-  \item{\dots}{
-    Placeholder for further arguments that might be needed by 
-    future implementations.
-  }
-  \item{alpha}{
-    The error tolerance for the decision limit (critical value).
-  }
-  \item{beta}{
-    The error tolerance beta for the detection limit.
-  }
-  \item{method}{
-    The default method uses a prediction interval at the LOD
-    for the estimation of the LOD, which obviously requires
-    iteration. This is described for example in Massart, p. 432 ff.
-    The \dQuote{din} method uses the prediction interval at
-    x = 0 as an approximation.
-  }
-}
-\value{
-  A list containig the corresponding x and y values of the estimated limit of
-  detection of a model used for calibration.  
-}
-\description{
-  The decision limit (German: Nachweisgrenze) is defined as the signal or
-  analyte concentration that is significantly different from the blank signal
-  with a first order error alpha (one-sided significance test).
-  The detection limit, or more precise, the minimum detectable value 
-  (German: Erfassungsgrenze), is then defined as the signal or analyte
-  concentration where the probability that the signal is not detected although
-  the analyte is present (type II or false negative error), is beta (also a
-  one-sided significance test).
-}
-\note{
-  - The default values for alpha and beta are the ones recommended by IUPAC.
-  - The estimation of the LOD in terms of the analyte amount/concentration
-    xD from the LOD in the signal domain SD is done by simply inverting the
-    calibration function (i.e. assuming a known calibration function).
-  - The calculation of a LOD from weighted calibration models requires
-    a weights argument for the internally used \code{\link{predict.lm}}
-    function, which is currently not supported in R.
-}
-\references{
-  Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong, S., Lewi, P.J., 
-  Smeyers-Verbeke, J. (1997) Handbook of Chemometrics and Qualimetrics: Part A,
-  Chapter 13.7.8 
-
-  J. Inczedy, T. Lengyel, and A.M. Ure (2002) International Union of Pure and
-  Applied Chemistry Compendium of Analytical Nomenclature: Definitive Rules.
-  Web edition.
-
-  Currie, L. A. (1997) Nomenclature in evaluation of analytical methods including
-  detection and quantification capabilities (IUPAC Recommendations 1995). 
-  Analytica Chimica Acta 391, 105 - 126.
-}
-\examples{
-data(din32645)
-m <- lm(y ~ x, data = din32645)
-lod(m) 
-
-# The critical value (decision limit, German Nachweisgrenze) can be obtained
-# by using beta = 0.5:
-lod(m, alpha = 0.01, beta = 0.5)
-}
-\seealso{
-  Examples for \code{\link{din32645}}  
-}
-\keyword{manip}