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        <title>A new very simply explicitly invertible approximation for the standard normal cumulative distribution function</title>
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    <abstract>\textlessabstract\textgreater\textlessp\textgreaterThis paper proposes a new very simply explicitly invertible function to approximate the standard normal cumulative distribution function (CDF). The new function was fit to the standard normal CDF using both MATLAB’s Global Optimization Toolbox and the BARON software package. The results of three separate fits are presented in this paper. Each fit was performed across the range $ 0 \textbackslashleq z \textbackslashleq 7 $ and achieved a maximum absolute error (MAE) superior to the best MAE reported for previously published very simply explicitly invertible approximations of the standard normal CDF. The best MAE reported from this study is 2.73e–05, which is nearly a factor of five better than the best MAE reported for other published very simply explicitly invertible approximations.\textless/p\textgreater\textless/abstract\textgreater</abstract>
    <identifier type="citekey">Lipoth-2022-A</identifier>
    <identifier type="doi">10.3934/math.2022648</identifier>
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        <date>2022</date>
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%0 Journal Article
%T A new very simply explicitly invertible approximation for the standard normal cumulative distribution function
%A Lipoth, Jessica
%A Tereda, Yoseph
%A Papalexiou, Simon Michael
%A Spiteri, Raymond J.
%J AIMS Mathematics, Volume 7, Issue 7
%D 2022
%V 7
%N 7
%I American Institute of Mathematical Sciences (AIMS)
%F Lipoth-2022-A
%X \textlessabstract\textgreater\textlessp\textgreaterThis paper proposes a new very simply explicitly invertible function to approximate the standard normal cumulative distribution function (CDF). The new function was fit to the standard normal CDF using both MATLAB’s Global Optimization Toolbox and the BARON software package. The results of three separate fits are presented in this paper. Each fit was performed across the range $ 0 \textbackslashleq z \textbackslashleq 7 $ and achieved a maximum absolute error (MAE) superior to the best MAE reported for previously published very simply explicitly invertible approximations of the standard normal CDF. The best MAE reported from this study is 2.73e–05, which is nearly a factor of five better than the best MAE reported for other published very simply explicitly invertible approximations.\textless/p\textgreater\textless/abstract\textgreater
%R 10.3934/math.2022648
%U https://gwf-uwaterloo.github.io/gwf-publications/G22-59001
%U https://doi.org/10.3934/math.2022648
%P 11635-11646

Markdown (Informal)

[A new very simply explicitly invertible approximation for the standard normal cumulative distribution function](https://gwf-uwaterloo.github.io/gwf-publications/G22-59001) (Lipoth et al., GWF 2022)

• A new very simply explicitly invertible approximation for the standard normal cumulative distribution function (Lipoth et al., GWF 2022)

ACL

• Jessica Lipoth, Yoseph Tereda, Simon Michael Papalexiou, and Raymond J. Spiteri. 2022. A new very simply explicitly invertible approximation for the standard normal cumulative distribution function. AIMS Mathematics, Volume 7, Issue 7, 7(7):11635–11646.