High Accurate Simple Approximation of Normal Distribution Integral
Joint Authors
Sarmiento-Reyes, Arturo
Sanchez Orea, Jesus
Filobello-Niño, Uriel
Vazquez-Leal, Hector
Castañeda-Sheissa, Roberto
Source
Mathematical Problems in Engineering
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-22, 22 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-02-08
Country of Publication
Egypt
No. of Pages
22
Main Subjects
Abstract EN
The integral of the standard normal distribution function is an integral without solution and representsthe probability that an aleatory variable normally distributed has values between zero and x.
The normaldistribution integral is used in several areas of science.
Thus, this work provides an approximate solutionto the Gaussian distribution integral by using the homotopy perturbation method (HPM).
After solvingthe Gaussian integral by HPM, the result served as base to solve other integrals like error function and thecumulative distribution function.
The error function is compared against other reported approximationsshowing advantages like less relative error or less mathematical complexity.
Besides, some integrals relatedto the normal (Gaussian) distribution integral were solved showing a relative error quite small.
Also, theutility 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 implementthe approximate error function.
American Psychological Association (APA)
Vazquez-Leal, Hector& Castañeda-Sheissa, Roberto& Filobello-Niño, Uriel& Sarmiento-Reyes, Arturo& Sanchez Orea, Jesus. 2012. High Accurate Simple Approximation of Normal Distribution Integral. Mathematical Problems in Engineering،Vol. 2012, no. 2012, pp.1-22.
https://search.emarefa.net/detail/BIM-1029483
Modern Language Association (MLA)
Vazquez-Leal, Hector…[et al.]. High Accurate Simple Approximation of Normal Distribution Integral. Mathematical Problems in Engineering No. 2012 (2012), pp.1-22.
https://search.emarefa.net/detail/BIM-1029483
American Medical Association (AMA)
Vazquez-Leal, Hector& Castañeda-Sheissa, Roberto& Filobello-Niño, Uriel& Sarmiento-Reyes, Arturo& Sanchez Orea, Jesus. High Accurate Simple Approximation of Normal Distribution Integral. Mathematical Problems in Engineering. 2012. Vol. 2012, no. 2012, pp.1-22.
https://search.emarefa.net/detail/BIM-1029483
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1029483