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

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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.

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The authors confirm that the data supporting the findings of this study are available within the article and its supplementary materials.

Notes

  1. We observed that the present version of the software package R (Version 4.2.2) is able to invert all the values in Table 4.

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Acknowledgements

The authors are grateful to the referee for carefully evaluating the manuscript and for their suggestions and comments, enhancing the readability and quality of the paper. The first author is thankful to the Council of Scientific and Industrial Research India (Grant No. 09/1022(11054)/2021-EMR-I) for the financial support.

Funding

Council of Scientific and Industrial Research India (CSIR) provided financial support for Dhivya Prabhu K for this research.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Indore, Indore, 453552, Madhya Pradesh, India

    Dhivya Prabhu K, Sanjeev Singh & Antony Vijesh V

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  1. Dhivya Prabhu K
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  2. Sanjeev Singh
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  3. Antony Vijesh V
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All figures and tables were prepared by K. Dhivya Prabhu. All authors wrote and reviewed the manuscript.

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Correspondence to Antony Vijesh V.

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K, D.P., Singh, S. & V, A.V. A third-order iterative algorithm for inversion of cumulative central beta distribution. Numer Algor 94, 1331–1353 (2023). https://doi.org/10.1007/s11075-023-01537-6

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