A logistic approximation to the cumulative normal distribution
This paper develops a logistic approximation to the cumulative normal distribution. Although the literature contains a vast collection of approximate functions for the normal distribution, they are very complicated, not very accurate, or valid for only a limited range. This paper proposes an enhance...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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OmniaScience
2009-07-01
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| Series: | Journal of Industrial Engineering and Management |
| Subjects: | |
| Online Access: | http://www.jiem.org/index.php/jiem/article/view/60 |
| _version_ | 1811281455735635968 |
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| author | Shannon R. Bowling Mohammad T. Khasawneh Sittichai Kaewkuekool Byung Rae Cho |
| author_facet | Shannon R. Bowling Mohammad T. Khasawneh Sittichai Kaewkuekool Byung Rae Cho |
| author_sort | Shannon R. Bowling |
| collection | DOAJ |
| description | This paper develops a logistic approximation to the cumulative normal distribution. Although the literature contains a vast collection of approximate functions for the normal distribution, they are very complicated, not very accurate, or valid for only a limited range. This paper proposes an enhanced approximate function. When comparing the proposed function to other approximations studied in the literature, it can be observed that the proposed logistic approximation has a simpler functional form and that it gives higher accuracy, with the maximum error of less than 0.00014 for the entire range. This is, to the best of the authors’ knowledge, the lowest level of error reported in the literature. The proposed logistic approximate function may be appealing to researchers, practitioners and educators given its functional simplicity and mathematical accuracy. |
| first_indexed | 2024-04-13T01:33:59Z |
| format | Article |
| id | doaj.art-284f94e8ec0f419991be1cb747a5e14c |
| institution | Directory Open Access Journal |
| issn | 2013-8423 2013-0953 |
| language | English |
| last_indexed | 2024-04-13T01:33:59Z |
| publishDate | 2009-07-01 |
| publisher | OmniaScience |
| record_format | Article |
| series | Journal of Industrial Engineering and Management |
| spelling | doaj.art-284f94e8ec0f419991be1cb747a5e14c2022-12-22T03:08:26ZengOmniaScienceJournal of Industrial Engineering and Management2013-84232013-09532009-07-012111412710.3926/jiem..v2n1.p114-12726A logistic approximation to the cumulative normal distributionShannon R. Bowling0Mohammad T. Khasawneh1Sittichai Kaewkuekool2Byung Rae Cho3Old Dominion UniversityState University of New York - BinghamtonKing Mongkut’s University of Technology ThonburiClemson UniversityThis paper develops a logistic approximation to the cumulative normal distribution. Although the literature contains a vast collection of approximate functions for the normal distribution, they are very complicated, not very accurate, or valid for only a limited range. This paper proposes an enhanced approximate function. When comparing the proposed function to other approximations studied in the literature, it can be observed that the proposed logistic approximation has a simpler functional form and that it gives higher accuracy, with the maximum error of less than 0.00014 for the entire range. This is, to the best of the authors’ knowledge, the lowest level of error reported in the literature. The proposed logistic approximate function may be appealing to researchers, practitioners and educators given its functional simplicity and mathematical accuracy.http://www.jiem.org/index.php/jiem/article/view/60normal distributionlogisticapproximationminimax criteria |
| spellingShingle | Shannon R. Bowling Mohammad T. Khasawneh Sittichai Kaewkuekool Byung Rae Cho A logistic approximation to the cumulative normal distribution Journal of Industrial Engineering and Management normal distribution logistic approximation minimax criteria |
| title | A logistic approximation to the cumulative normal distribution |
| title_full | A logistic approximation to the cumulative normal distribution |
| title_fullStr | A logistic approximation to the cumulative normal distribution |
| title_full_unstemmed | A logistic approximation to the cumulative normal distribution |
| title_short | A logistic approximation to the cumulative normal distribution |
| title_sort | logistic approximation to the cumulative normal distribution |
| topic | normal distribution logistic approximation minimax criteria |
| url | http://www.jiem.org/index.php/jiem/article/view/60 |
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