A New Special Function and Its Application in Probability
In this note we present a new special function that behaves like the error function and we provide an approximated accurate closed form for its CDF in terms of both Chèbyshev polynomials of the first kind and the error function. Also we provide its series representation using Padé approximant. We sh...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2018/5146794 |
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| _version_ | 1832566845214818304 |
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| author | Zeraoulia Rafik Alvaro H. Salas David L. Ocampo |
| author_facet | Zeraoulia Rafik Alvaro H. Salas David L. Ocampo |
| author_sort | Zeraoulia Rafik |
| collection | DOAJ |
| description | In this note we present a new special function that behaves like the error function and we provide an approximated accurate closed form for its CDF in terms of both Chèbyshev polynomials of the first kind and the error function. Also we provide its series representation using Padé approximant. We show a convincing numerical evidence about an accuracy of 10-6 for the approximants in the sense of the quadratic mean norm. A similar approach may be applied to other probability distributions, for example, Maxwell–Boltzmann distribution and normal distribution, such that we show its application using both of those distributions. |
| format | Article |
| id | doaj-art-a0f1c649cf454c3390ba727a1a58f78a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-a0f1c649cf454c3390ba727a1a58f78a2025-02-03T01:03:05ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252018-01-01201810.1155/2018/51467945146794A New Special Function and Its Application in ProbabilityZeraoulia Rafik0Alvaro H. Salas1David L. Ocampo2University Batna, AlgeriaUniversidad Nacional de Colombia, ColombiaUniversidad Nacional de Colombia, ColombiaIn this note we present a new special function that behaves like the error function and we provide an approximated accurate closed form for its CDF in terms of both Chèbyshev polynomials of the first kind and the error function. Also we provide its series representation using Padé approximant. We show a convincing numerical evidence about an accuracy of 10-6 for the approximants in the sense of the quadratic mean norm. A similar approach may be applied to other probability distributions, for example, Maxwell–Boltzmann distribution and normal distribution, such that we show its application using both of those distributions.http://dx.doi.org/10.1155/2018/5146794 |
| spellingShingle | Zeraoulia Rafik Alvaro H. Salas David L. Ocampo A New Special Function and Its Application in Probability International Journal of Mathematics and Mathematical Sciences |
| title | A New Special Function and Its Application in Probability |
| title_full | A New Special Function and Its Application in Probability |
| title_fullStr | A New Special Function and Its Application in Probability |
| title_full_unstemmed | A New Special Function and Its Application in Probability |
| title_short | A New Special Function and Its Application in Probability |
| title_sort | new special function and its application in probability |
| url | http://dx.doi.org/10.1155/2018/5146794 |
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