Properties and approximations of a Bessel distribution for data science applications
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916868799856640 |
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| author | Bonamente, Massimiliano |
| author_facet | Bonamente, Massimiliano |
| contents | 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 $χ^2_1$-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 $χ^2_2$-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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_21812 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Properties and approximations of a Bessel distribution for data science applications Bonamente, Massimiliano Methodology Instrumentation and Methods for Astrophysics 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 $χ^2_1$-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 $χ^2_2$-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. |
| title | Properties and approximations of a Bessel distribution for data science applications |
| topic | Methodology Instrumentation and Methods for Astrophysics |
| url | https://arxiv.org/abs/2507.21812 |