The implicit power function is defined as follows:
Power of the test=1-CDF(alpha, h,r, LBNP)
where CDF stands for the cumulative distribution function of non-central F-distribution. The solution of the above function for the non-centrality parameter yields the LBNP. This value is used in geodetic problems for two aims:
To optimize a geodetic network or experiment such that the predicted non-centrality parameter is greater than or equal to LBNP,
To figure out the minimal detectable bias (MDB), minimum detectable displacement (MDD), minimum detectable velocity (MDV), minimum detectable amplitude (MDA) (or any parameters to be tested with F-test) in the designed geodetic network or experiment.
Please refer to the following studies for further reading:
Aydin C (2012). Power of global test in deformation analysis, Journal of Surveying Engineering (ASCE), 10.1061/(asce)su.1943-5428.0000064
Aydin C and Demirel H (2005). Computation of Baarda's lower bound of the non-centrality parameter, Journal of Geodesy, 10.1007/s00190-004-0406-1
Aydin C and Gunes O (2024). Power function of F-distribution: Revisiting its computation and solution for geodetic studies, Journal of Geodesy, 98, 10.1007/s00190-024-01905-7