Some improvements for existing simple Approximations of the Normal Distribution Function

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-09-09 DOI:10.18187/pjsor.v18i3.4007

A. Hanandeh, Omar M. Eidous

引用次数: 1

Abstract

Due to the widespread applicability and use of the normal distribution, a need has arisen to approximate its cumulative distribution function (cdf). In this article, five new simple approximations to the standard normal cdf are developed. In order to assess the accuracy of the proposed approximations, both maximum absolute error and mean absolute error were used. The maximum absolute errors of the proposed approximations lie between 0.00095 and 0.00946, which is highly accurate if compared to the existing simple approximations and quite sufficient for many real-life applications. Even though simple approximations may not as accurate as complicated ones, they are, though, fairly good when judged vis-a-vis their simplicity.

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对现有的正态分布函数的简单近似作了一些改进

由于正态分布的广泛适用性和使用，需要对其累积分布函数(cdf)进行近似。在这篇文章中，开发了5种新的简单的近似标准正态cdf。为了评估所提出的近似的准确性，使用了最大绝对误差和平均绝对误差。所提出的近似的最大绝对误差介于0.00095和0.00946之间，与现有的简单近似相比，这是非常精确的，对于许多实际应用来说已经足够了。尽管简单的近似可能不如复杂的精确，但相对于它们的简单性而言，它们还是相当不错的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.