Computation of Baarda’s lower bound of the non-centrality parameter

Abstract.

Baarda’s reliability measures for outliers, as well as sensitivity and separability measures for deformations, are functions of the lower bound of the non-centrality parameter (LBNP). This parameter, which is taken from Baarda’s well-known nomograms, is actually a non-centrality parameter of the cumulative distribution function (CDF) of the non-central χ²-distribution yielding a complementary probability of the desired power of the test, i.e. probability of Type II error. It is investigated how the LBNP can be computed for desired probabilities (power of the test and significance level) and known degrees of freedom. Two recursive algorithms, namely bisection and the Newton algorithm, were applied to compute the LBNP after the definition of a stable and accurate algorithm for the computation of the corresponding CDF. Despite the fact that the recursive algorithms ensure some desired accuracy, it is presented numerically that the Newton algorithm has a faster convergence to the solution than the bisection algorithm.