The cumulative distribution function (CDF) of the doubly non-central beta distribution can be expressed as an infinite double series. By truncating the sum of this series, one can obtain an approximate value of the CDF. Although numerous methods exist for calculating the non-central beta distribution, which allow for the control of the truncation range and estimation of the computational error, no such methods have been developed for the doubly non-central beta distribution. In this paper, we propose two new numerical computation methods based on the segmentation of the infinite double series, termed DIV1 and DIV2. Both methods enable automated calculations once the error control parameters are set; there is no need to predetermine the truncation range, and their computational times are comparable. Following detailed derivations, we have established the upper bounds of the errors for both methods, thus ensuring the determinability of the precision.

翻译：双重非中心Beta分布的累积分布函数（CDF）可以表示为无限双级数。通过截断该级数的和，可以获得CDF的近似值。尽管存在多种计算非中心Beta分布的方法，这些方法允许控制截断范围并估计计算误差，但针对双重非中心Beta分布尚未开发出此类方法。本文提出了两种基于无限双级数分割的新数值计算方法，分别称为DIV1和DIV2。两种方法在设定误差控制参数后均可实现自动计算；无需预先确定截断范围，且计算时间相当。经过详细推导，我们建立了两种方法的误差上界，从而确保了精度的可确定性。