Solution for the Indefinite Integral of the Standard Normal Probability Density Function

2015/12/15 by Joram Soch, Soch, Joram
Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #FOS: Mathematics #Other Statistics (stat.OT) #Probability and Risk Models #Statistical Distribution Estimation and Applications #Statistics Theory (math.ST) #math.ST #stat.OT #stat.TH

paper · pdf · doi:10.48550/arxiv.1512.04858

6 pages, 1 figure (caption corrected)

openalex publication_date 2015/12/15 · openalex created_date 2016/06/24 · arxiv created 2016/11/04 · arxiv updated 2016/11/07 · openalex updated_date 2026/07/28

Abstract

Conventional wisdom assumes that the indefinite integral of the probability density function for the standard normal distribution cannot be expressed in finite elementary terms. While this is true, there is an expression for this anti-derivative in infinite elementary terms that, when being differentiated, directly yields the standard normal density function. We derive this function using infinite partial integration and review its relation to the cumulative distribution function for the standard normal distribution and the error function.

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