This paper presents properties and approximations of a random variable based on the zero–order modified Bessel function that results from the compounding of a zero-mean Gaussian with a χ12-distributed variance. This family of distributions is a special case of the McKay family of Bessel distributions and of a family of generalized Laplace distributions. It is found that the Bessel distribution can be approximated with a null-location Laplace distribution, which corresponds to the compounding of a zero-mean Gaussian with a χ22-distributed variance. Other useful properties and representations of the Bessel distribution are discussed, including a closed form for the cumulative distribution function that makes use of the modified Struve functions. Another approximation of the Bessel distribution that is based on an empirical power-series approximation is also presented. The approximations are tested with the application to the typical problem of statistical hypothesis testing. It is found that a Laplace distribution of suitable scale parameter can approximate quantiles of the Bessel distribution with better than 10% accuracy, with the computational advantage associated with the use of simple elementary functions instead of special functions. It is expected that the approximations proposed in this paper be useful for a variety of data science applications where analytic simplicity and computational efficiency are of paramount importance.
| Published in | International Journal of Statistical Distributions and Applications (Volume 11, Issue 3) |
| DOI | 10.11648/j.ijsda.20251103.11 |
| Page(s) | 85-97 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2025. Published by Science Publishing Group |
Bessel Distribution, Laplace Distribution, Generalized Laplace Distribution, Gaussian Distribution, Variance- gamma Distribution, Compounding of Random Variables, Hypothesis Testing
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APA Style
Bonamente, M. (2025). Properties and Approximations of a Bessel Distribution for Data Science Applications. International Journal of Statistical Distributions and Applications, 11(3), 85-97. https://doi.org/10.11648/j.ijsda.20251103.11
ACS Style
Bonamente, M. Properties and Approximations of a Bessel Distribution for Data Science Applications. Int. J. Stat. Distrib. Appl. 2025, 11(3), 85-97. doi: 10.11648/j.ijsda.20251103.11
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Download@article{10.11648/j.ijsda.20251103.11,
author = {Massimiliano Bonamente},
title = {Properties and Approximations of a Bessel Distribution for Data Science Applications
},
journal = {International Journal of Statistical Distributions and Applications},
volume = {11},
number = {3},
pages = {85-97},
doi = {10.11648/j.ijsda.20251103.11},
url = {https://doi.org/10.11648/j.ijsda.20251103.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsda.20251103.11},
abstract = {This paper presents properties and approximations of a random variable based on the zero–order modified Bessel function that results from the compounding of a zero-mean Gaussian with a χ12-distributed variance. This family of distributions is a special case of the McKay family of Bessel distributions and of a family of generalized Laplace distributions. It is found that the Bessel distribution can be approximated with a null-location Laplace distribution, which corresponds to the compounding of a zero-mean Gaussian with a χ22-distributed variance. Other useful properties and representations of the Bessel distribution are discussed, including a closed form for the cumulative distribution function that makes use of the modified Struve functions. Another approximation of the Bessel distribution that is based on an empirical power-series approximation is also presented. The approximations are tested with the application to the typical problem of statistical hypothesis testing. It is found that a Laplace distribution of suitable scale parameter can approximate quantiles of the Bessel distribution with better than 10% accuracy, with the computational advantage associated with the use of simple elementary functions instead of special functions. It is expected that the approximations proposed in this paper be useful for a variety of data science applications where analytic simplicity and computational efficiency are of paramount importance.
},
year = {2025}
}
TY - JOUR T1 - Properties and Approximations of a Bessel Distribution for Data Science Applications AU - Massimiliano Bonamente Y1 - 2025/08/05 PY - 2025 N1 - https://doi.org/10.11648/j.ijsda.20251103.11 DO - 10.11648/j.ijsda.20251103.11 T2 - International Journal of Statistical Distributions and Applications JF - International Journal of Statistical Distributions and Applications JO - International Journal of Statistical Distributions and Applications SP - 85 EP - 97 PB - Science Publishing Group SN - 2472-3509 UR - https://doi.org/10.11648/j.ijsda.20251103.11 AB - This paper presents properties and approximations of a random variable based on the zero–order modified Bessel function that results from the compounding of a zero-mean Gaussian with a χ12-distributed variance. This family of distributions is a special case of the McKay family of Bessel distributions and of a family of generalized Laplace distributions. It is found that the Bessel distribution can be approximated with a null-location Laplace distribution, which corresponds to the compounding of a zero-mean Gaussian with a χ22-distributed variance. Other useful properties and representations of the Bessel distribution are discussed, including a closed form for the cumulative distribution function that makes use of the modified Struve functions. Another approximation of the Bessel distribution that is based on an empirical power-series approximation is also presented. The approximations are tested with the application to the typical problem of statistical hypothesis testing. It is found that a Laplace distribution of suitable scale parameter can approximate quantiles of the Bessel distribution with better than 10% accuracy, with the computational advantage associated with the use of simple elementary functions instead of special functions. It is expected that the approximations proposed in this paper be useful for a variety of data science applications where analytic simplicity and computational efficiency are of paramount importance. VL - 11 IS - 3 ER -
Department of Physics and Astronomy, University of Alabama in Huntsville, Huntsville, USA
