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

被引：12
作者：
Prabhu, K. Dhivya [1 ]
Singh, Sanjeev [1 ]
Vijesh, V. Antony [1 ]
机构：
[1] Indian Inst Technol Indore, Dept Math, Indore 453552, Madhya Pradesh, India
来源：
NUMERICAL ALGORITHMS | 2023年 / 94卷 / 03期
关键词：
Cumulative central beta distribution; F distribution; Newton method; Quantile function; Schwarzian derivative; Student's t distribution; NEWTONS METHOD; ZEROS; CONVERGENCE; VARIANT;
D O I：
10.1007/s11075-023-01537-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：1331 / 1353
页数：23
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