Statistical properties of limit of detection test statistics

There are a number of possible ways to define the instrumental limit of detection (LOD) figure of merit and in the present work we define four such sample test statistics and derive their probability density functions (PDFs). Although the derived PDFs were found to be irreducible integrals, they are easily evaluated via numerical integration and can be used to obtain expectation values, population precisions and confidence intervals. Monte Carlo simulation methods were used to prepare normalized histograms of one million LOD variates each, for homoscedastic linear calibration curve systems, and these were found to be in excellent agreement with the numerically obtained PDFs and associated statistics. The software used in all aspects of the present work is available for free, with full, commented source code, and is designed to facilitate exploration of calibration curve systems of immediate interest to the reader.