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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", tol = "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 \dQuote{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.
+  }
+  \item{tol}{
+    When the \dQuote{default} method is used, the default tolerance
+    for the LOD on the x scale is the value of the smallest non-zero standard
+    divided by 1000. Can be set to a numeric value to override this.
+  }
+}
+\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}