A third-order iterative algorithm for inversion of cumulative central beta distribution

Abstract

An efficient third-order iterative method for inverting the cumulative central beta distribution numerically is proposed. First, a third-order iterative method for finding zeros of the solution of second-order homogeneous linear ODEs is designed. This method is derived by approximating the integration obtained from the second-order ODE. The method is exact for any function f with a constant logarithmic derivative of f′ . Sufficient conditions are obtained to ensure the nonlocal convergence of the proposed method. As an application, an interesting numerical algorithm is obtained for inverting the cumulative central beta distribution. To demonstrate the proposed theory, numerical simulation results were presented and compared with the existing algorithms. © 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.