Error-controlled algorithm for the cumulative distribution function of doubly non-central F distribution

Abstract

The doubly non-central F distribution is a widely applied probability distribution. The cumulative distribution function (CDF) of the doubly non-central F distribution can be expressed using the infinite doubly series. In this paper, a CDF calculation method that allows for controlled precision is derived through the study of the infinite doubly series. By setting parameters, this method can provide an upper limit of error for the computed results, thereby allowing for precision control in the calculations. Experimental results demonstrate that this method achieves a good balance between computational precision and speed.