Approximating the Mode of the Non-Central Chi-Squared Distribution

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DOI: https://doi.org/10.28924/2291-8639-20-2022-19
Published: Mar 30, 2022
Cite as:
V. Ananiev, A. L. Read, Approximating the Mode of the Non-Central Chi-Squared Distribution, Int. J. Anal. Appl., 20 (2022), 19.

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V. Ananiev, A. L. Read

Abstract

In this paper we consider the probability density function (pdf) of the non-central χ2 distribution with arbitrary number of degrees of freedom and non-centrality. For this function we find the approximate location of the maximum and discuss related edge cases of 1 and 2 degrees of freedom. We also use this expression to demonstrate the improved performance of the C++ Boost’s implementation of the non-central χ2 and extend the domain of its applicability.

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