Research Article
Properties and Approximations of a Bessel Distribution for Data Science Applications
Massimiliano Bonamente*
Issue:
Volume 11, Issue 3, September 2025
Pages:
85-97
Received:
9 March 2025
Accepted:
21 March 2025
Published:
5 August 2025
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.
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 dist...
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