High Accurate Simple Approximation of Normal Distribution Integral. (8th February 2012)

• Record Type: Journal Article
• Authors: Vazquez-Leal, Hector; Castaneda-Sheissa, Roberto; Filobello-Nino, Uriel; Sarmiento-Reyes, Arturo; Sanchez Orea, Jesus
• Other Names: Nohara Ben T. Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2012(2012)
• Publication Date: 2012-02-08
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2012/124029
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : The integral of the standard normal distribution function is an integral without solution and represents the probability that an aleatory variable normally distributed has values between zero and x . The normal distribution integral is used in several areas of science. Thus, this work provides an approximate solution to the Gaussian distribution integral by using the homotopy perturbation method (HPM). After solving the Gaussian integral by HPM, the result served as base to solve other integrals like error function and the cumulative distribution function. The error function is compared against other reported approximations showing advantages like less relative error or less mathematical complexity. Besides, some integrals related to the normal (Gaussian) distribution integral were solved showing a relative error quite small. Also, the utility for the proposed approximations is verified applying them to a couple of heat flow examples. Last, a brief discussion is presented about the way an electronic circuit could be created to implement the approximate error function.