Characteristic Function of the Tsallis <i>q</i>-Gaussian and Its Applications in Measurement and Metrology
The Tsallis <i>q</i>-Gaussian distribution is a powerful generalization of the standard Gaussian distribution and is commonly used in various fields, including non-extensive statistical mechanics, financial markets and image processing. It belongs to the <i>q</i>-distribution...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Metrology |
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| Online Access: | https://www.mdpi.com/2673-8244/3/2/12 |
| _version_ | 1797593511797719040 |
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| author | Viktor Witkovský |
| author_facet | Viktor Witkovský |
| author_sort | Viktor Witkovský |
| collection | DOAJ |
| description | The Tsallis <i>q</i>-Gaussian distribution is a powerful generalization of the standard Gaussian distribution and is commonly used in various fields, including non-extensive statistical mechanics, financial markets and image processing. It belongs to the <i>q</i>-distribution family, which is characterized by a non-additive entropy. Due to their versatility and practicality, <i>q</i>-Gaussians are a natural choice for modeling input quantities in measurement models. This paper presents the characteristic function of a linear combination of independent <i>q</i>-Gaussian random variables and proposes a numerical method for its inversion. The proposed technique makes it possible to determine the exact probability distribution of the output quantity in linear measurement models, with the input quantities modeled as independent <i>q</i>-Gaussian random variables. It provides an alternative computational procedure to the Monte Carlo method for uncertainty analysis through the propagation of distributions. |
| first_indexed | 2024-03-11T02:09:11Z |
| format | Article |
| id | doaj.art-5ff9008fe6bd4508ba9fa714acd63ce2 |
| institution | Directory Open Access Journal |
| issn | 2673-8244 |
| language | English |
| last_indexed | 2024-03-11T02:09:11Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Metrology |
| spelling | doaj.art-5ff9008fe6bd4508ba9fa714acd63ce22023-11-18T11:37:44ZengMDPI AGMetrology2673-82442023-05-013222223610.3390/metrology3020012Characteristic Function of the Tsallis <i>q</i>-Gaussian and Its Applications in Measurement and MetrologyViktor Witkovský0Institute of Measurement Science, Slovak Academy of Sciences, Dúbravská Cesta 9, 841 04 Bratislava, SlovakiaThe Tsallis <i>q</i>-Gaussian distribution is a powerful generalization of the standard Gaussian distribution and is commonly used in various fields, including non-extensive statistical mechanics, financial markets and image processing. It belongs to the <i>q</i>-distribution family, which is characterized by a non-additive entropy. Due to their versatility and practicality, <i>q</i>-Gaussians are a natural choice for modeling input quantities in measurement models. This paper presents the characteristic function of a linear combination of independent <i>q</i>-Gaussian random variables and proposes a numerical method for its inversion. The proposed technique makes it possible to determine the exact probability distribution of the output quantity in linear measurement models, with the input quantities modeled as independent <i>q</i>-Gaussian random variables. It provides an alternative computational procedure to the Monte Carlo method for uncertainty analysis through the propagation of distributions.https://www.mdpi.com/2673-8244/3/2/12Tsallis q-Gaussian distributioncharacteristic functionnumerical inversionlinear measurement modelmeasurement uncertainty |
| spellingShingle | Viktor Witkovský Characteristic Function of the Tsallis <i>q</i>-Gaussian and Its Applications in Measurement and Metrology Metrology Tsallis q-Gaussian distribution characteristic function numerical inversion linear measurement model measurement uncertainty |
| title | Characteristic Function of the Tsallis <i>q</i>-Gaussian and Its Applications in Measurement and Metrology |
| title_full | Characteristic Function of the Tsallis <i>q</i>-Gaussian and Its Applications in Measurement and Metrology |
| title_fullStr | Characteristic Function of the Tsallis <i>q</i>-Gaussian and Its Applications in Measurement and Metrology |
| title_full_unstemmed | Characteristic Function of the Tsallis <i>q</i>-Gaussian and Its Applications in Measurement and Metrology |
| title_short | Characteristic Function of the Tsallis <i>q</i>-Gaussian and Its Applications in Measurement and Metrology |
| title_sort | characteristic function of the tsallis i q i gaussian and its applications in measurement and metrology |
| topic | Tsallis q-Gaussian distribution characteristic function numerical inversion linear measurement model measurement uncertainty |
| url | https://www.mdpi.com/2673-8244/3/2/12 |
| work_keys_str_mv | AT viktorwitkovsky characteristicfunctionofthetsallisiqigaussiananditsapplicationsinmeasurementandmetrology |