A Simple Approximation to the Area Under Standard Normal Curve
By Amit Choudhury. 2014
23 citations recorded by the source corpus.
Of all statistical distributions, the standard normal is perhaps the most popular and widely used. Its use often involves computing the area under its probability curve. Unlike many other statistical distributions, there is no closed form theoretical expression for this area in case of the normal distribution. Consequently it has to be approximated. While there are a number of highly complex but accurate algorithms, some simple ones have also been proposed in literature. Even though the simple ones may not be very accurate, they are nevertheless useful as accuracy has to be gauged vis-a-vis simplicity. In this short paper, we present another simple approximation formula to the cumulative distribution function of standard normal distribution. This new formula is fairly good when judged vis-a-vis its simplicity.
Subfields: Finance, Mathematical Physics, Statistics and Probability, Numerical Methods & Scientific Computing
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Citations in the corpus
- Gaussian Error Linear Units (GELUs) (2016, neutral): “044715 x 3 )]) (Choudhury, 2014) 1 or xσ (1 .”
- Transforming the Area under the Normal Curve (AUC) into Cohen’s d, Pearson’s rpb, Odds-Ratio, and Natural Log Odds-Ratio: Two Conversion Tables (2018, background): “There are also a large number of mathematical functions for converting AUC into z, and vice versa (e.g., Brophy, 1983; 1985; Bryc, 2002; Choudhury, 2014; Emerson, 1979; Hart, 1957; 1966; Polya, 1945; Zelen & Severo, 1964).”
- Bridging Nonlinearities and Stochastic Regularizers with Gaussian Error Linear Units (2016, background): “044715x)]) is a sufficiently fast, easy-to-implement approximation [2].”