Open AccessApproximating the Mode of the Non-Central Chi-Squared Distribution
Author(s) -
V. Ananiev,
A. L. Read
Publication year - 2022
Publication title -
international journal of analysis and applications
Language(s) - English
Resource type - Journals
ISSN - 2291-8639
DOI - 10.28924/2291-8639-20-2022-19
Subject(s) - mathematics , centrality , degrees of freedom (physics and chemistry) , probability density function , mode (computer interface) , function (biology) , domain (mathematical analysis) , distribution (mathematics) , enhanced data rates for gsm evolution , mathematical analysis , statistics , computer science , artificial intelligence , physics , quantum mechanics , evolutionary biology , biology , operating system
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.