Two Precision-controlled Numerical Algorithms forthe CDF of Doubly Non-central Beta DistributionBased on the Segmentation of the Infinite DoubleSeries Matrix

The cumulative distribution function (CDF) of the doubly non-central beta distribution can be expressed as an infinite doubleseries. By truncating the sum of this series, one can obtain an approximate value of the CDF. Although numerous methodsexist for calculating the non-central beta distribution, which allow for the control of the truncation range and estimation of thecomputational error, no such methods have been developed for the doubly non-central beta distribution. In this paper, wepropose two new numerical computation methods based on the segmentation of the infinite double series, termed DIV1 andDIV2. Both methods enable automated calculations once the error control parameters are set; there is no need to predeterminethe truncation range, and their computational times are comparable. Following detailed derivations, we have established theupper bounds of the errors for both methods, thus ensuring the determinability of the precision.