Abstract
The mean of a noncentral chi random variable is usually expressed in terms a hypergeometric function. On a 17 pages paper, Lawrence [Sankhyā A. https://doi.org/10.1007/s13171-021-00262-3] derived simpler expressions for the mean, involving the modified Bessel function of the first kind and the error function. We show here that these expressions follow immediately from known relationships between the hypergeometric and modified Bessel / error functions.
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References
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995). Continuous Univariate Distributions, 2, 2nd edn. Wiley, New York.
Lawrence, J. (2021). Moments of the noncentral chi distribution. Sankhyā A. https://doi.org/10.1007/s13171-021-00262-3.
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SC wrote Section 1. The remaining sections were written by SN.
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Nadarajah, S., Chan, S. On Moments of the Noncentral Chi Distribution. Sankhya A 85, 803–807 (2023). https://doi.org/10.1007/s13171-022-00278-3
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DOI: https://doi.org/10.1007/s13171-022-00278-3