What question did this study set out to answer?

The aim is to develop accurate and efficient analytical approximations for the inverse error function and the cumulative distribution function.

May 24, 2026AppliedMathOpen Access

New Handy and Accurate Approximation for the Inverse Error Function and Cumulative Distribution Integrals with Applications

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Analytical approximations improve accuracy of cumulative distribution functions, suggesting practical uses in engineering and statistics.

The aim is to develop accurate and efficient analytical approximations for the inverse error function and the cumulative distribution function.
Utilized the Power Series Extender Method (PSEM) to derive the approximations
Demonstrated high accuracy particularly in the central region of the domain
Presented two case studies to illustrate practical applications in statistical analysis and engineering
Achieved high accuracy of approximations across a wide domain, particularly in central regions
Maintained a compact expression using elementary functions, enhancing practical implementation
Showed improved accuracy through the use of strategically selected cancellation points, especially in key areas

Sandoval-Hernandez et al. (2026) studied this question.

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