The power function of \(F-\) distribution is the complementary cumulative distribution function of the non-central \(F-\) distribution. It is used to evaluate the power of the test based on the \(F\) or \({\chi }^{2}-\) distributed statistics. This paper revisits its computation and solution for the non-centrality parameter in geodetic studies and shows that the power function related to these studies can be computed efficiently and with minimal effort. To facilitate this, we introduce a novel standalone algorithm that consistently computes the power of the test, even for large non-centrality parameters (e.g., \(>{10}^{5}\)) and for \({\chi }^{2}\)-distribution. The solution of the power function for the non-centrality parameter is typically obtained using standard root finding algorithms, such as the bisection or Newton–Raphson methods. However, they may encounter convergence problems, particularly when the non-centrality parameter increases. We demonstrate that a solution can be readily obtained from a logarithmic form of the power function, ensuring convergence and removing the requirement for a precisely defined initial value. Furthermore, we utilize a few geometric relationships during the iteration to expedite the solution process. As a result, we propose a novel solution algorithm that is highly precise, stable, and at least four times faster than standard algorithms, even for the solution interval of \(<{0, 10}^{6}>\). This efficient solution is published online as a web-based application for geodetic detectability studies in addition to the given MATLAB and Python codes.

\（F-\） 分布的幂函数是非中心分布 \（F-\） 的互补累积分布函数。它用于根据 \（F\） 或 \（{\chi }^{2}-\） 分布统计数据评估测试的功效。本文重新审视了大地测量研究中非中心性参数的计算和求解，并表明与这些研究相关的幂函数可以高效且省力地计算。为了促进这一点，我们引入了一种新的独立算法，它可以始终如一地计算测试的功效，即使对于大型非中心性参数（例如，\（>{10}^{5}\））和 \（{\chi }^{2}\） 分布也是如此。非中心性参数的幂函数解通常使用标准求根算法获得，例如二分法或 Newton-Raphson 方法。但是，它们可能会遇到收敛问题，尤其是在非中心性参数增加时。我们证明，可以很容易地从幂函数的对数形式中获得解，确保收敛并消除对精确定义的初始值的要求。此外，我们在迭代过程中利用了一些几何关系来加快求解过程。因此，我们提出了一种新的求解算法，该算法具有高度精确、稳定且至少比标准算法快四倍的算法，即使求解区间为 \（<{0， 10}^{6}>\） 也是如此。除了给定的 MATLAB 和 Python 代码外，这种高效的解决方案还作为基于 Web 的应用程序在线发布，用于大地测量可探测性研究。