Some Simple Full-Range Inverse-Normal Approximations
Two approximations are given for numerically inverting the full range of the standard normal cumulative distribution function. The first approximation has two fitted constants and only modest accuracy but is very simple and well suited for hand calculators. The second approximation has four fitted...
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| Language: | English |
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Publishing House of the Romanian Academy
2025-01-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
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| Online Access: | https://www.ictp.acad.ro/jnaat/journal/article/view/1434 |
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| author | Raymond Koopman |
| author_facet | Raymond Koopman |
| author_sort | Raymond Koopman |
| collection | DOAJ |
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Two approximations are given for numerically inverting the full range of the standard normal cumulative distribution function. The first approximation has two fitted constants and only modest accuracy but is very simple and well suited for hand calculators. The second approximation has four fitted constants and is more accurate. Alternate versions of the approximations are also given, with the constants chosen to minimize the maximum relative error in the implied approximate q rather than the maximum absolute error in the approximate z.
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| format | Article |
| id | doaj-art-56ca746f359c4d2b92dd537f613ef521 |
| institution | Kabale University |
| issn | 2457-6794 2501-059X |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj-art-56ca746f359c4d2b92dd537f613ef5212025-02-10T14:49:36ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2025-01-0110.33993/jnaat541-1434Some Simple Full-Range Inverse-Normal ApproximationsRaymond Koopman0https://orcid.org/0000-0003-3977-8939Simon Fraser University, Canada Two approximations are given for numerically inverting the full range of the standard normal cumulative distribution function. The first approximation has two fitted constants and only modest accuracy but is very simple and well suited for hand calculators. The second approximation has four fitted constants and is more accurate. Alternate versions of the approximations are also given, with the constants chosen to minimize the maximum relative error in the implied approximate q rather than the maximum absolute error in the approximate z. https://www.ictp.acad.ro/jnaat/journal/article/view/1434numerical approximationinverse normal distribution functioninverse error function |
| spellingShingle | Raymond Koopman Some Simple Full-Range Inverse-Normal Approximations Journal of Numerical Analysis and Approximation Theory numerical approximation inverse normal distribution function inverse error function |
| title | Some Simple Full-Range Inverse-Normal Approximations |
| title_full | Some Simple Full-Range Inverse-Normal Approximations |
| title_fullStr | Some Simple Full-Range Inverse-Normal Approximations |
| title_full_unstemmed | Some Simple Full-Range Inverse-Normal Approximations |
| title_short | Some Simple Full-Range Inverse-Normal Approximations |
| title_sort | some simple full range inverse normal approximations |
| topic | numerical approximation inverse normal distribution function inverse error function |
| url | https://www.ictp.acad.ro/jnaat/journal/article/view/1434 |
| work_keys_str_mv | AT raymondkoopman somesimplefullrangeinversenormalapproximations |