Two error controllable computing algorithms for the CDF of doubly non-central beta distribution

Since the cumulative distribution function(CDF) of the doubly non-central beta distribution can be represented by the infinite double series, therefore, truncating the summation of the series can obtain the approximate value of CDF. The existing numerical computation methods must specify the truncating range and cannot estimate the calculation error. In this paper, two new numerical computation methods based on the division on the infinite double series, named DIV1 and DIV2, are proposed. Both methods can perform automated calculations after configuring the error control lines, the truncating range does not need to be determined, and their computation times are comparable. After detailed derivation, the upper error bounds of both methods are obtained, which means that the accuracy of the two methods can be determined precisely. Therefore, this paper recommends two methods to calculate the CDF of the doubly non-central beta distribution.